In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each point using values of rr such that r≥0 and values of θ such that 0≤θ<2π. Visually check your answers to ensure they make sense.
(x,y)=(2,5) corresponds to (r,θ)=
(x,y)=(−3,3) corresponds to (r,θ)=
(x,y)=(−5,−3.5) corresponds to (r,θ)=
(x,y)=(0,−5.4)corresponds to (r,θ)=
Answers
Step-by-step explanation:
We have cartisean points. We are trying to find polar points.
We can find r by applying the pythagorean theorem to the x value and y values.
[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]
And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.
[tex] \tan(x) = \frac{y}{x} [/tex]
Remeber since we are trying to find the angle measure, use inverse tan function
[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]
Answers For 2,5
[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]
So r=sqr root of 29
[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]
So the answer is (sqr root of 29,68).
For -3,3
[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]
[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]
Use the identity
[tex] \tan(x) = \tan(x + \pi) [/tex]
So that means
[tex] \tan(x) = 135[/tex]
So our points are
(3 times sqr root of 2, 135)
For 5,-3.5
[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]
[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]
So our points are (sqr root of 37.25, 35)
For (0,-5.4)
[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]
So r=5.4
[tex] \tan {}^{ - 1} (0) = undefined[/tex]
So our points are (5.4, undefined)
Related Questions
a) What is 10% of 40 ?
b) What number is 10% more than 40 ?
Answers
The expression 10% of 40 is 4 and 10% more than 40 is 44
(a) What is 10% of 40?From the question, we have the following parameters that can be used in our computation:
10% of 40
Express "of" as products
So, we have
10% of 40 = 10% * 40
Evaluate
10% of 40 = 4
b) What number is 10% more than 40?In this case, we have:
10% more than 40
This means that
10% more than 40 = 40 * (1 + 10%)
Evaluate
10% more than 40 = 44
Hence. 10% more than 40 is 44
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on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?
Answers
Answer:
15.5
Step-by-step explanation:
Pepe= 2/3 x 12 = 8
Paula= 1/4 x 30 = 7.5
8+7.5=15.5
find a polynomial function whose graph passes through (7,11) (11,-12) and (0,4)
Answers
The polynomial function whose graph passes through (7,11) (11,-12) and (0,4) will be y = -0.614x² + 5.295x + 4.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Assume the polynomial function is quadratic. Then the equation is given as,
y = ax² + bx + c
At (0, 4), we have
4 = a(0)² + b(0) + c
c = 4
Then the equation is written as,
y = ax² + bx + 4
At (7, 11), we have
y = ax² + bx + 4
11 = 49a + 7b + 4 ...1
At (11, -12), we have
- 12 = 121a + 11b + 4 ...2
Equations 1 and 2 are solved by a calculator. Then we have
a = - 0.614 and b = 5.295
The polynomial capability whose diagram goes through (7,11) (11,- 12) and (0,4) will be y = - 0.614x² + 5.295x + 4.
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Based on the figure given below.
AC = 20cm
BC = 24Cm
AB = 16cm
CD = 15Cm and CE = 18cm then
a) Show that triangle ABC sim triangle DEC
b) How long is DC ?
Answers
Answer:
Step-by-step explanation:
A.) To show that triangle ABC is similar to triangle DEC, we need to prove that the ratios of the sides of the two triangles are equal.
First, we can write the ratios of the sides of triangle ABC as follows:
AC/AB = 20/16 = 5/4
BC/AB = 24/16 = 3/2
Now, we can write the ratios of the sides of triangle DEC as follows:
CE/CD = 18/15 = 6/5
AC/CD = 20/15 = 4/3
Since the ratios of the sides of the two triangles are equal, it follows that triangle ABC is similar to triangle DEC.
B.) To find the length of DC, we can use the fact that triangle ABC is similar to triangle DEC. Since the ratios of the sides of the two triangles are equal, we can set up a proportion to solve for DC.
First, we can write the ratio of the sides of triangle ABC as follows:
AC/AB = DC/CE
Then, we can substitute the known values for AC, AB, and CE:
20/16 = DC/18
Then, we can cross-multiply to solve for DC:
DC = (20/16) * 18
= (5/4) * 18
= 45/4
= 11.25 cm
Therefore, the length of DC is approximately 11.25 cm.
Answer:
Step-by-step explanation:
To show that triangle ABC is analogous to triangle DEC, we need to prove that the rates of the sides of the two triangles are equal.
First, we can write the rates of the sides of triangle ABC as follows
AC/ AB = 20/16 = 5/4
BC/ AB = 24/16 = 3/2
Now, we can write the rates of the sides of triangle DEC as follows
CE/ CD = 18/15 = 6/5
AC/ CD = 20/15 = 4/3
Since the rates of the sides of the two triangles are equal, it follows that triangle ABC is analogous to triangleDEC.
B.) To find the length of DC, we can use the fact that triangle ABC is analogous to triangle DEC. Since the rates of the sides of the two triangles are equal, we can set up a proportion to break for DC.
First, we can write the rate of the sides of triangle ABC as follows
AC/ AB = DC/ CE
also, we can substitute the known values for AC, AB, and CE
20/16 = DC/ 18
also, we cancross-multiply to break for DC
DC = (20/16) * 18
= (5/4) * 18
= 45/4
= 11.25 cm
Thus, the length of DC is roughly11.25 cm.
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a duck flew at 18 miles per hour for 3 hours than at 15 miles per hour for 2 ours how far did the duck fly in all
Answers
The distance the duck fly in all is 99 miles
How to determine how far the duck fly in allFrom the question, we have the following parameters that can be used in our computation:
Distance 1: 18 miles per hour for 3 hoursDistance 2: 15 miles per hour for 2 hoursThe distance covered in all can be calculated as
Distance = The sum of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance = 18 * 3 + 15 * 2
Evaluate the products
This gives
Distance = 54 + 45
Evaluate the sum
Distance = 99 miles
Hence, the distance is 99 miles
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Staci pays $32.70 for 5 cell phone cases. Each case costs the same amount. How much does each case cost?
Part A
Which expression represents the problem?
$32.70 × 5
$32.70 ÷ 5
$32.70 + 5
$32.70 – 5
Part B
Evaluate the expression from Part A.
$ ( ??? )
Answers
Answer:
$32.70 ÷ 5
Each case is $6.54.
Step-by-step explanation:
$3270 for 5 cases, meaning you would split $32.70 into 5.
$32.70 ÷ 5 phone cases = $6.54
This also means each case is $6.54. To prove this, multiply by 5.
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $35. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1825. How many tickets of each type were sold?
Answers
Answer:
sorry i messed up my first calculations, currently recalculating
Step-by-step explanation:
Answer:
35 same-day tickets20 advance ticketsStep-by-step explanation:
You want the number of $30 advance tickets and $35 same-day tickets sold, when a total of 55 tickets were sold for $1825.
SetupLet s represent the number of same-day tickets sold. Then 55-s is the number of advance tickets sold, and total revenue is ...
35s +30(55 -s) = 1825
Solution5s = 175 . . . . . . Simplify, subtract 1650
s = 35
55-s = 30
35 same-day and 30 advance tickets were sold.
Which of the following represents members of the domain of the graphed function?
See attached picture
Responses
{-4, 2, 3}
{-4, 0, 1}
{1, 2, 3, 4}
{1, 2, 3, 5}
Answers
The {-4, 0, 1} represents members of the domain of the graphed function.
What is the domain of the function?
A function is a mathematical object that accepts input, appears to apply a rule to it, and returns the result.
A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result.
The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs.
The range refers to the outputs which are actually used.
Domain: {-4, 0, 1}.
Simply list the domain as -4 < x < 2, which would imply ALL values between -4 and 2 inclusive.
Yes, this is a function. No x-values repeat, and it passes the Diagonal Line Test for functions.
Hence, the {-4, 0, 1} represents members of the domain of the graphed function.
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Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. Select the correct answer below and fill in the answer box to complete your choice. O A. According to the Divergence Test, the series converges because lim ak = k- 00 (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim ax = kos (Simplify your answer.) OC. The Divergence Test is inconclusive because lim ak (Simplify your answer.) OD. The Divergence Test is inconclusive because lim ak does not exist.
Answers
The Divergence Test is inconclusive because lim ak = ∞
The Divergence Test is used to determine whether a given infinite series converges or diverges.
In order to use the Divergence Test, we must examine the limit of the terms of the series as n approaches infinity.
In the given series, the limit of the terms as n approaches infinity is not defined. Therefore, the Divergence Test is inconclusive.
The Divergence Test is inconclusive because lim ak = ∞
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For each of these lists of integers, find a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
f ) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
Answers
The simple formula or rule that generates the terms of an integer sequence that begins with the given list is given below.
What is sequence?Sequence is the order in which elements, such as numbers, letters, or symbols, follow one another in a specific order. It is a fundamental concept in mathematics and computer science, and is used in many other areas including music, language, and art. In mathematics, it is often used to describe patterns or to represent numerical values. In computer science, it is used to represent data structures, such as lists and arrays.
a. The sequence can be expressed as 3x2^n, where n is the position of the number in the sequence. The next three terms are 127, 162, and 201.
b. The sequence can be expressed as 4n+3, where n is the position of the number in the sequence. The next three terms are 47, 51, and 55.
c. The sequence can be expressed as 2^n+n-1, where n is the position of the number in the sequence. The next three terms are 1111, 10000, and 10011.
d. The sequence can be expressed as the number of times the previous value is repeated, starting with 1. The next three terms are 5, 5, and 8.
e. The sequence can be expressed as 4x3^n, where n is the position of the number in the sequence. The next three terms are 5906, 17718, and 53154.
f. The sequence can be expressed as (n+1)!+(n-1)!+2, where n is the position of the number in the sequence. The next three terms are 27027025, 94594500, and 34459425.
g. The sequence can be expressed as the number of times the previous number is repeated, starting with 1. The next three terms are 0, 0, and 1.
h. The sequence can be expressed as 4^n, where n is the position of the number in the sequence. The next three terms are 4294967296, 17179869184, and 68719476736.
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Complete questions as follows-
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
a. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .
b. 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .
c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
d. 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .
e. 0, 2, 8, 26, 80,242,728,2186,6560,19682, . . .
f. 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
g. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .
h. 2, 4, 16, 256, 65536, 4294967296, . . .
a persons weight varies directly with gravity if a person weights 180 pounds on earth they will weigh only 30 pounds on the moon if harsh weights 54 pounds on earth how much would he weight on the moon
Answers
The weight of harsh on the moon if he weighs 54 pounds on earth is 9 pounds
How to calculate direct variation?Weight varies directly with gravity
Let
Weight of a person = w
Gravity = g
So,
w = k × g
Where,
k = constant of proportionality
If w = 180 pounds and g = 30 pounds
w = k × g
180 = k × 30
180 = 30k
divide both sides by 30
k = 180/30
k = 6
If w = 54 pounds g = ?
w = k × g
54 = 6 × g
54 = 6g
divide both sides by 6
g = 54/6
g = 9 pounds
Therefore, harsh weighs 9 pounds on the moon.
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Determine the population mean, variance, and standard deviation for the set of data. (Round your answers to two decimal places.)
3, 6, 8, 12, 13, 15
mean variance standard deviation
Answers
Given the set of data, we can calculate that the mean is 9.5, the variance is 17.58 and the standard deviation is 4.19
Mean, variance, and standard deviation
The concepts of mean, variance and standard deviation are very basic but very important in statistics.
Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.
σ = [tex]\sqrt{variance}[/tex]
Now we can calculate the mean of the given data as follows:
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
= (3 + 6 + 8 + 12 + 13 + 15) / 6
= 57 / 6
= 9.5
Then we can calculate the variance as follows:
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
= [tex]\frac{((3-9,5)^{2} + (6-9,5)^{2} + (8-9,5)^{2} + (12-9,5)^{2} + (13-9,5)^{2} + (15-9,5)^{2} )}{6}[/tex]
= (42,25 + 12,25 + 2,25 + 6,25 + 12,25 + 30,25) / 6
= 105.5 / 6
= 17.58
Standard deviation can be calculated from the variance:
σ = [tex]\sqrt{variance}[/tex]
= [tex]\sqrt{17.58}[/tex]
= 4.19
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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x) = 2x + 4ex
Answers
After integration, the required function f is (2x³ - sin (x) + Cx + D).
What is the integration of 'xⁿ' and 'sin (x)'?
[tex]\int {x^{n} } \, dx = \frac{x^{n+1} }{n+1} + C\\\\\\\int {sinx} \, dx = -cosx + C[/tex]
Given, f''(x) = 12x + sin x
Therefore,
[tex]\int {f''(x)} \, dx \\\\=\int {f'(x)} \, dx \\\\\\= \int{12x + sin x} \, dx + C\\\\= 6x^{2} - cosx + C\\[/tex]
Again, f'(x) = 6x - cos (x) + C
Therefore,
[tex]\int {f'(x)} \, dx\\ \\=\int {f(x)} \, dx \\\\= \int {6x^{2} - cosx + C } \, dx \\\\= 2x^{3} - sinx + Cx + D[/tex]
Therefore, the required function is (2x³ - sin (x) + Cx + D).
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10. ANEW ACAR. Solve for x and CR. *
X=
Given: ANEW ACAR
NE = 11
EW = 12
I
AR = 4y - 12
CA = 4x + 3
NW = x + y
Answers
Applying the definition of congruent triangles, the values of x and y are:
x = 2; y = 6
Length of CR = 8 units.
How to Find the Sides of Congruent Triangles?If two triangles are congruent to each other, based on the CPCTC, all their corresponding angles, and their corresponding sides will be equal to each other.
Given that triangles NEW and CAR are congruent to each other, therefore:
NE = CA
NW = CR
EW = AR
Given the following measures:
NE = 11
EW = 12
AR = 4y - 12
CA = 4x + 3
NW = x + y
Therefore:
NE = CA
11 = 4x + 3
Solve for x:
11 - 3 = 4x
8 = 4x
8/4 = x
x = 2
EW = AR
12 = 4y - 12
12 + 12 = 4y
24 = 4y
24/4 = y
y = 6
NW = CR = x + y
Plug in the values of x and y:
CR = 2 + 6
CR = 8 units.
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+ 5 = 12
X =
Answers
Answer: 7
Step-by-step explanation:
x=12-5
x=7
Answer:
x=7
Step-by-step explanation:
12-5=7 or 7+5=12
Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are 17576 ways to perform steps 1-3, and there are 10000 ways to perform the remaining steps. Thus, the number of license plates is 175760000 (b) How many license plates could begin with A and end in 0? and the number of ways to place the 0 in the In this case, the number of ways to place the A in Step 1 is 1 final step is 1 . Thus, the answer is 676000 (c) How many license plates could begin with BWC? In this case, the number of ways to perform steps 1-3 is ___ Thus, the answer is ___(d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Enter an exact number
Answers
the total number of license plate is 17576000 and In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1' thus the total answer is 67600
What is permutation and combination?In mathematics, there are two alternative methods for dividing up a collection of items into subsets: combinations and permutations. Any order may be used by a combination to list the subset's elements. An ordered list of a subset's components is called a permutation.
There are [tex]26^3[/tex] = 17576, ways to perform step 1-3, and there are [tex]10^3[/tex] = 1000, ways to perform remaining steps .
the total number of license plate is 17576000
In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1'
thus the total answer is 67600
26 X 25 X 24 X 10 X 9 X 8 = 11232000
24 X 10 X 9 X 8 = 17280
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The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15
minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84
shoppers per hour make a purchase and each of these shoppers spends an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers,
on average, are waiting in the checkout line to make a purchase at the Good Deals Store
Answers
Note that at any time during business hours, about 7 shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store. This is solved using Little Law.
What is littles Law?Little's Law asserts that the long-term average number of individuals in a stable system, L, is equal to the long-term average effective arrival rate,λ, multiplied by the average duration a customer spends in the system, W.
To compute,
First, let's make sure that all the variables use the same time unit.
Thus, if there are 84 shoppers who are making a purchase per house, then there will be: 84/60 minutes
= 1.4
This means that λ (rate) = 1.4 and the average time (W) is 5 minutes
Using Little's Law which states that the queuing formula is:
L = λW
Note that:
λ = 1.4 (computed)
W = 5 mintues (given)
Hence, the Average number of people in queue per time is:
L = 1.4 x 5
L = 7 shoppers.
Thus, it is correct to state that at any time during work hours, about 7 shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store.
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Full Question:
If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?
PLS HELP
Select the correct answer.
A museum curator estimates that 85% of people who attend the museum would return a second time. She randomly surveys
50 people and finds that only 75% indicate that they would return a second time. So she decides to randomly survey an additional
100 people.
if her model is valld, what could she expect from the 150 total survey results?
The difference between the data and the model will get larger.
The difference between the data and the model will stay the same.
O it is impossible to predict how the difference between the data and the model will change
The difference between the data and the model will get smaller.
O
Submit
Answers
The difference between the model and the data will get smaller.
What is the sample size?A sample is a percentage of the total population in statistics. You can use the data from a sample to make inferences about a population as a whole.
Given here, she 50 people and finds that only 75% and additional 100 people hence changing the sample size
As our sample size increases, the confidence in our estimate increases, our uncertainty decreases and we have greater precision. Thus with the increase in sample size, the data would move closer to the estimated probability.
Hence The difference between the model and the data will get smaller.
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Answer:
The difference between the data and the model will get smaller.
Step-by-step explanation:
Plato/Edmentum
Consider the reaction: SO2(g) + 1/2 O2(g)SO3(g) Write the equilibrium constant for this reaction in terms of the equilibrium constants, and , for the reactions below: 2 S(s) + 3 O2(g) 2 SO3(g) S(s) + O2(g) SO2(g) For answers with both a subscript and a superscript, enter the subscript first. For example, enter K12 if the first equilibrium constant should be squared. K =
Answers
the equilibrium constant for this reaction in terms of the equilibrium constants is Knet = √Ka/Kb
and for the reactions below:
2 S(s) + 3 O2(g) 2 SO3(g) is √Ka
S(s) + O2(g) SO2(g) is 1/Kb
A reversible reaction mechanism progresses from initial conditions to chemical equilibrium at a constant temperature, with all reactants and products present in constant non-zero amounts. At this temperature, an equilibrium constant "K" exists. It is frequently followed by a subscript to indicate the type of equilibrium constant that it considers depending on the phases of reaction species that it considers. The expression for each type of equilibrium constant differs with the direction and stoichiometry of the balanced reaction equation. This enables existing equations with known "K" values to be exploited in order to derive new "K" values for related systems.
SO2(g) + 1/2 O2(g)SO3 (g) is the desired reaction equation
We consider the first given reaction system at the bottom. We divide its coefficients by two to get the square root of the initial equilibrium constant: 2 S(s) + 3 O2(g) (g) 2 SO3(g) = √Ka
Then we reverse the second given reaction system at the bottom. Its current equilibrium constant is the reciprocal of the predecessor: S(s) + O2(g) SO2(g) is 1/Kb
The above two equations total to yield our target equation. The product of the two values obtained above yields the target equilibrium constant: Knet = √Ka/Kb
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What are the values of u and v?
u = ?°
v = ?°
Answers
u=94
You have to multiple 43 by 2 you would get 86 so now you would have to subtract that from 180 and would get 94
You have to subtract 64 from 180 and you would get 116 so now you would have to divide it by 2 and you would get 58
Can someone please solve this problem for me.
Answers
The cost of one chair is [tex]x=54.75[/tex] $ and the cost of one table is [tex]y=49.5[/tex] $.
What is the total cost?
The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total. The formula is:
Total cost = (Average fixed cost x average variable cost)
Let cost of one chair is [tex]x[/tex]
Let cost of one table is [tex]y[/tex]
So,
[tex]5x+3y=31[/tex] ...(1)
[tex]2x+6y=52[/tex] ......(2)
Solving equation (1) and (2) we get
[tex]a_1x+b_1y+x_1=0\\\\a_2x+b_2y+c_2=0[/tex]
[tex]\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}\\\\\frac{x}{3(31)-6(52)}=\frac{y}{31(2)-52(5)}=\frac{1}{5(2)-2(3)}\\\\\frac{x}{93-312}=\frac{y}{62-260}=\frac{1}{10-6}\\\\\frac{x}{-219}=\frac{y}{-198}=\frac{1}{-4}\\\\x=54.75,y=49.5[/tex]
Hence, the cost of one chair is [tex]54.75[/tex] $ and the cost of one table is [tex]49.5[/tex] $.
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What is as a fraction?
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A fraction means a part of something or a number of parts of something. The number on the bottom shows how many parts something has been divided into ½ means 1 part of something that has been divided into 2 parts. We call this a half. If you add two halves together you get one.
Answer: A fraction is a numerical quantity that is not a whole number
Step-by-step explanation:
The two-way frequency table contains data about students' preferred exercise.
Enjoys swimming Enjoys cycling Row totals
Likes running 28 62 90
Does not like running 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who do not like to run but enjoy cycling?
64%
55%
32%
23%
Answers
The joint relative frequency for those students who don't like to run, but however enjoy cycling, is C. 32%.
How to find the joint frequency ?The joint frequency for students who like cycling, but do not like running, can be found by the formula :
= Number of students who enjoy cycling but don't enjoy running / Number of students in total
Number of students who enjoy cycling but don't enjoy running = 64
Number of students in total = 200
The joint frequency is :
= 64 / 200 x 100%
= 0.32 x 100 %
= 32 %
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Write an equation for the line through the given point with the given slope in slope-intercept form. (10, –9); m = –2
Please explain.
Answers
Considering the definition of a line, the equation of the line that passes through the point (10, -9) and has a slope of -2 is y= -2x +11.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of -2.The line passes through the point (10, -9).Substituting the value of the slope m and the value of the point y=mx+b, the value of the ordinate to the origin b is obtained as follow:
-9= -2×10 + b
-9= -20 + b
-9 + 20= b
11= b
Finally, the equation of the line is y= -2x +11.
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Tom weighs 5kg more than Harry. Harry weighs 3kg more than Freddie who, in turn weighs
2 kg less than Alfie. What is the difference, in kilograms, between Tom and Alfie?
Answers
The difference between Tom and Alfie is 1 kg
Let's call the weight of Tom T, the weight of Harry H, the weight of Freddie F, and the weight of Alfie A. We are given that T = H + 5, H = F + 3, and F = A - 2.
Substituting the second and third equations into the first equation gives us:
T = (A - 2) + 3 + 5
T = A - 2 + 3 + 5
T = A + 1
So the difference between Tom and Alfie is T - A = A + 1 - A = 1 kg.
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The square of a number is equal to 72 more than the number. Find all such numbers.
Answers
Answer:
You just need to think about this a little. There is a number, that you don't know, x, and if you square it ([tex]x^2[/tex]), that value will be equal to 72 more than the unknown number itself, so you put that into an equation.
Step-by-step explanation:
[tex]x^2=x+72\\x^2-x-72=0\\[/tex]
Apply quadratic formula (you can look it up)
[tex]x_1=\frac{-(-1)+\sqrt{(-1)^2+(-4*1*-72} )}{2(1)} \\\\x_2=\frac{-(-1)-\sqrt{(-1)^2+(-4*1*-72} )}{2(1)} \\\\[/tex]
There are two answers to the quadratic formula.
The rest should be easy.
Here we show that function defined on an interval value property cannot have (a; b) and satisfying the intermediate removable or (a) jump discontinuity. Suppose has & jump discontinuity at Xo € (a,b) and lim f (x) lim f (x) xx0 {ix0 Choose 0 such that lim f (x) < 0 < lim f (x) and 0 + f(xo) xI*o Xx0 In Exercise & we showed there is interval [xo 0,.Xo) such that f(x) < 0 if Xe [xo 6,xo): Likewise, there an interval (xo, Xo + 6] such that f(x) > 0 if xe(xo, Xo + 6]. Conclude that does not satisly the intermediate value property on [xo 6,xXo + 6]. (6) Suppose has a removable discontinuity at Xo € (a,b) and a = lim f(x) < f(xo) Show that there is an interval [xo = 6,Xo) such that f(x)< a+[f(xo) - &] if x e[xo 6,Xo]: Conclude that f does not satisfy the intermediate value property
Answers
f cannot have a jump discontinuity at [tex]$x_0 \in(a, b)$[/tex] and [tex]$$ \lim _{x \uparrow x_0} f(x) < \lim _{x \mid x_0} f(x) .$$[/tex]
f cannot have a removable discontinuity at [tex]$$x_0 \in(a, b) $$[/tex] and [tex]\alpha=\lim _{x \rightarrow x_0} f(x) < f\left(x_0\right)[/tex]
Let f be a function defined on (a, b) satisfies intermediate value property.
Claim: f ca not have removable on jump discontinuity.
Suppose f has a jump discontinuity at [tex]$x_0 \in(a, b)$[/tex]
We take [tex]$\theta$[/tex] such that
[tex]$$\lim _{x \rightarrow x_0} f(x) < \theta < \lim _{x \downarrow x_0} f(x) \text { and } \theta \neq f\left(x_0\right)$$[/tex]
Now there exist [tex]$\delta > 0$[/tex] such that [tex]$f(x) < \theta$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right)$[/tex] and [tex]$f(x) > \theta$[/tex] for all [tex]$x \in\left(x_0, x_0+\delta\right]$[/tex]
Now [tex]$f\left(x_0-\delta\right)[/tex][tex]< \theta < f\left(x_0+\delta\right)$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0+\delta\right] \backslash\left\{x_2\right\}$[/tex] and [tex]$f\left(x_0\right) \neq \theta$[/tex].
Therefore the point [tex]$\theta$[/tex] has no preimage under f
that is, there does not exists [tex]$y \in\left[x_0-\delta, x_0+\delta\right][/tex] for which
[tex]$$f(y)=\theta[/tex] because [tex]\left\{\begin{array}{l}y=x_0 \Rightarrow f(y) \neq \theta \\y > x_0 \Rightarrow f(y) > \theta \\y < x_0 \Rightarrow f(y) < \theta\end{array}\right.$$[/tex]
Therefore f does not satisfies intermediate value property on [tex]$\left[x_0-\delta, x_0+\delta\right]$[/tex],
Hence f does not satisfies IVP on (a, b) which is not possible because we assume f satisfies IVP on (a, b),
Therefore f can not have a jump discontinuity.
Suppose f has a removable point of discontinuity at [tex]$x_0 \in(a, b)$[/tex],
Let [tex]$\alpha=\lim _{\alpha \rightarrow x_0} f(x)$[/tex],
Let [tex]\alpha < f\left(x_0\right)$[/tex] so [tex]$f\left(x_0\right)-\alpha > 0$[/tex].
Now [tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex] then [tex]\exists$ \delta > 0$[/tex] such that
[tex]$$\begin{aligned}& |f(x)-\alpha| < \frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left\{x_0-\delta, x_0-\alpha\right]-\left\{x_0\right\} \\& \Rightarrow \quad f(x) < \alpha+\frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left[x_0-\delta, x_0+\delta\right]-\left\{x_0\right\}\end{aligned}$$[/tex]
So [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2}$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right]-\left\{x_0\right\}$[/tex]
Now [tex]$f\left(x_0\right) > \alpha$[/tex].
And [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2} < f\left(x_0\right)$[/tex] for all [tex]$x \in\left[\left(x_0 \delta, x_0\right)\right.$[/tex]
Let [tex]$\mu=\frac{f\left(x_0\right)+\alpha}{2}$[/tex].
Then there does not exist [tex]$e \in\left[x_0-\delta, c\right]$[/tex] such that [tex]$f(c)=\mu$[/tex]
Because for [tex]$e=x_0 \quad f(e) > \mu$[/tex]
for [tex]$c < x_0 \quad f(c) < \mu$[/tex].
Therefore f does not satisfy IVP on [tex]$\left[x_0-\delta_1 x_0\right]$[/tex] which contradict our hypothesis,
therefore [tex]$\alpha \geqslant f\left(x_0\right)$[/tex]
Let [tex]$\alpha > f\left(x_0\right)$[/tex]. so [tex]$\alpha-f\left(x_0\right) > 0$[/tex]
[tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex]
Then [tex]\exists $ \varepsilon > 0$[/tex] such that
[tex]$|f(x)-\alpha| < \frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$\left.x \in\left[x_0-\varepsilon_0 x_0+\varepsilon\right]\right\}\left\{x_i\right\}$[/tex]
[tex]$\Rightarrow f(x) > \alpha-\frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0+\varepsilon\right] \backslash\left\{x_0\right\}$[/tex]
[tex]$\Rightarrow f(x) > \frac{\alpha+f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0\right)$[/tex]
Now [tex]$f\left(x_0\right) < \alpha$[/tex]
The [tex]$f(x) > \frac{f\left(x_0\right)+\alpha}{2} > f\left(x_0\right)$[/tex].
So [tex]$f\left(x_0\right) < \frac{f\left(x_0\right)+\alpha}{2} < f(x)$[/tex] for all [tex]$x \in\left[x_0 \varepsilon, \varepsilon_0\right)$[/tex]
Let [tex]$\eta=\frac{f\left(x_e\right)+\alpha}{2}$[/tex]
Then there does not exist [tex]$d \in\left[x_0-\varepsilon, x_0\right]$[/tex] such that [tex]$f(d)=\xi$[/tex].
Because if [tex]$d=x_0, f(d)=f\left(x_0\right) < \eta$[/tex] if [tex]$d E\left[x_0-\varepsilon, x_0\right)$[/tex]
Then [tex]$f(d) > \eta$[/tex]
Therefore f does not satisfies IVP on [tex]$\left[x_0-\varepsilon, x_0\right]$[/tex] which contradict olio hypothesis.
Therefore [tex]$\alpha \leq f\left(x_0\right)$[/tex] (b) From (a) and (b) it follows [tex]$\alpha=f\left(x_0\right)=\lim _{x \rightarrow x_0} f(x)$[/tex]. Therefore f can not have a removable discontinuous
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Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?
Answers
Total no. of cups of baking soda used for the experiment in improper fraction is [tex]\frac{91}{8}[/tex].
How much baking soda was used?Initial no. of cups of baking soda used for an experiment = [tex]1\frac{3}{4}[/tex]
Converting mixed fraction to improper fraction,
[tex]1\frac{3}{4}=\frac{7}{4}[/tex]
No. of times the experiment performed by students = [tex]6\frac{1}{2}[/tex]
Converting mixed fraction to improper fraction,
[tex]6\frac{1}{2} = \frac{13}{2}[/tex]
Total no. of cups of baking soda =(Initial no. of cups)* (No. of times)
[tex]=\frac{7}{4} *\frac{13}{2} \\\\=\frac{91}{8} \\\\[/tex]
= 11.4 (decimal form)
What is a mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like [tex]1\frac{3}{4}[/tex] is one where the remainder is 3 and the quotient is 1. Therefore, a mixed fraction is made up of both a full number and a correct fraction. A whole number and a legal fraction are both expressed together as a mixed number.A number between any two whole numbers is typically represented by it. Any fraction whose numerator exceeds or is equal to its denominator is considered improper. When the numerator value is less than the denominator, the fraction is said to be proper.To learn more about improper fraction, refer:
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NO LINKS!!
The expoential function given by f(x) = e^x called the (a. natural logarithmic, natural exponential, c. 1 to 1 exponential, d. 1 to 1 algebraic, e. transcendental algebraic) function and the base e is called the (a. algebraic, b. 1 to 1, c. natural, d. rational, e. transcendental)
Answers
Answer:
natural exponential
natural
quizlet
Answer:
b. natural exponential
c. natural
Step-by-step explanation:
Given function:
[tex]f(x)=e^x[/tex]
The given exponential function is called the:
natural exponential functionThe base e is called the:
natural baseThe number "e" occurs naturally in math and the physical sciences.
It is the base rate of growth shared by all continually growing processes, and so is called the natural base.
It is an irrational number and named after the 18th century Swiss mathematician, Leonhard Euler, and so is often referred to as "Euler's number".
5x^2-13+6=0
i need helppp
Answers
Answer:
answer is 2.5
Step-by-step explanation: