The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178
In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).
The derivative of r(t) with respect to t is:
r'(t) = <3, 2t, 3t^2>
The point (3, 1, 1) corresponds to t = 1,
and r′(1) = <3, 2(1), 3(1)^2>
r'(1) = <3, 2, 3>
|r'(1)| = √(3^2 + 2^2 + 3^2)
|r'(1)| = √(9 + 4 + 9)
|r'(1)| = √(22)
|r'(1)| = 4.69
Now, r''(t) = <0, 2, 6t>
and r′'(1) = <0, 2, 6(1)>
r''(1) = <0, 2, 6>
r′(1) × r′′(1) = <0, 4, 18>
|r′(1) × r′′(1) |
= √(0^2 + 4^2 + 18^2)
= √(16 + 324)
= √340
= 18.44
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 18.44 / 4.69³
k(1) = 0.178
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Given || m ||n, find the value of x.
124°
(5x-4)°
Answer:
x=12
Step-by-step explanation:
5x-4 is vertically opposite and 124 + 5x-4 should add up to 180 because they are cointerior anglesthen you look for the value of x by 124+5x-4=180
124-4+5x-4=180
x=12
Could the average peron lift the weight of $150 in quarter? HINT: The average quarter weigh 0. 2 oz
Answer: Yes, they can.
Step-by-step explanation: Since quarters weigh 0.2 oz. 1 dollar weighs 0.8 oz. 0.8x150=120oz. 120ozs is about 7.5 pounds, so yes.
3.50x+2(2.75)≤18 solve this please
Answer:
x ≤ 25/7
Step-by-step explanation:
3.5x + 5.5 ≤ 18
3.5x ≤ 18 - 5.5
3.5x ≤ 12.5
x ≤ 12.5/3.5
x ≤ 25/7
Select the graph for the solution of the open sentence. Click until the correct graph appears.
2|x| + 1 < 5
Answer:
graph C
Step-by-step explanation:
if x ≥ 0
2x + 1 < 5
2x < 5 - 1
2x < 4
2/2 x < 4/2
x < 2
0≤ x < 2
if x < 0
2 (-x) + 1 < 5
-2x < 5 - 1
-2x < 4
-2/-2 x > 4/-2
x > -2
-2 < x < 0
final solution
-2 < x < 2
Why in this case would we expect the sample size to be small? (Mark all that might apply:) There limited amount of time that bat keepers maybe able to devote to this activity. The sample size doesn't have to be small: There are many bats in the wild We wouldnt want to unnecessarily stress the animals. There is limited number of bats in captivity:
When it comes to researching bats in captivity, we expect the sample size to be small for a few reasons.
Firstly, there may be a limited amount of time that bat keepers are able to devote to this activity due to other obligations. Secondly, we would not want to unnecessarily stress the animals by collecting too many samples. Lastly, there is a limited number of bats in captivity, so the sample size will be small.
On the other hand, there are many bats in the wild, which means that the sample size does not have to be small. Researchers can take advantage of this by collecting data from a larger sample size. However, researchers must be mindful of the impact that their research may have on the environment, and the stress that it may cause the animals.
In conclusion, the sample size for studying bats in captivity is likely to be small due to the limited amount of time that bat keepers can devote to this activity, the need to avoid unnecessarily stressing the animals, and the limited number of bats in captivity. On the other hand, a larger sample size is possible when studying bats in the wild, but researchers must be mindful of the impact of their research on the environment and the animals.
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What is the equation of the line that is parallel to y = one-fifth x + 4 and that passes through (5,–4)?
On a coordinate plane, a line goes through (0, 4) and (5, 5). A point is at (5, negative 4).
y = negative 5 x minus 29
y = negative 5 x + 21
y = one-fifth x minus 4
y = one-fifth x minus 5
answer y=1/5x-5
Answer:
D) y = one-fifth x minus 5 ( or y = 1/5x - 5 )-------------------------------
Parallel lines have equal slopes.
Given line has a slope of m = 1/5.
Use point-slope form and the coordinates of the point (5, - 4) find the parallel line:
y - (- 4) = 1/5(x - 5)y + 4 = 1/5x - 1y = 1/5x - 1 - 4y = 1/5x - 5Correct choice is D.
The height of a stack of DVD cases is in a proportional relationship to the number of cases in the stack. A stack of 6 cases and its height are shown. Find the constant of proportionality. Then use the constant of proportionality to find the height of a stack of 14 cases. The height of 6 DVD cases is 114 mm.
pls help and ty
Answer:
lol
Step-by-step explanation:
hahahaha
help me pleasee find constant rate of change for the graph
Answer: B
Step-by-step explanation:
Let's pick 2 points ( 0,80) ( 5, 70)
The rate of change or slope is rise/run
We see that the y decrease by 10 and x increases by 5, so the slope is
-10/5 = -2 ft/s
So the aswer is B
The formula for the surface area of a cylinder open at both ends S= pi r l where l is the length
Solve the formula
Answer:
l = S / (2*pi*r)
[tex]l = \frac{S}{2\pi r}[/tex]
Step-by-step explanation:
S = 2 pi * r * l
Then:
l = S / (2*pi*r)
l = length
pi = 3.1416
r = radius
S = surface
Do 1.7 and 1.700 have the same value? In a full sentence, explain why or why not.
Answer: Yes.
Step-by-step explanation:
1.7 divided by 1.700 is 1
Or Find the miing number o that the equation ha infinitely many olution. – 3x–20= – 3x
For the equation -3x - 20 to have an infinite solution, it should be equal to -3x + 20 = -3x + 20, so the blank will be + 20
Given the data in the question,
Let the equation be - 3x + 20 = - 3x blank
These situations could be turned into producing an infinite number of solutions only if the lines are coincident and have the same y-intercept.
The quantities being coincident demonstrates the equality of the expressions printed on the left and right sides.
The lines with the same slopes are equal lines.
If the lines are making equal patterns, they will be giving infinite answers as output. As we can see in the result the equations are containing infinite solutions.
So, the missing blank will be = +20 to make the equation have infinite solutions.
Therefore, the value of the blank will be +20 and the equation will be =
- 3x + 20 = - 3x + 20
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Based on the given diagram, prove ABC is congruent to CDA by filling out the flowchart below.
The details of the angles in the diagram used to prove the congruency of the triangles ΔABC ≅ ΔCDA indicates;
Statements [tex]{}[/tex] Reasons
1. ∠D ≅ ∠B [tex]{}[/tex] 1. Given
∠ACB ≅ ∠CAD
2. Therefore; ∠ACD ≅ ∠CAB [tex]{}[/tex] 2. Angle sum property of a triangle
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex] [tex]{}[/tex] 3. Reflexive property
4. ΔABC ≅ ΔCDA [tex]{}[/tex] 4. ASA congruency rule
Therefore, the completed flowchart is presented as follows;
∠D ≅ ∠B [tex]{}[/tex] ∠ACB ≅ ∠CAB [tex]{}[/tex][tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]
∠ACB ≅ ∠CAB Angle sum property Reflexive prop
Reason; Given
[tex]{}[/tex] ΔABC ≅ ΔCDA
[tex]{}[/tex]
What are congruent triangles?
Triangles are congruent if the three sides on both triangles are congruent or if two angles and a non included side in one triangle are congruent to two angles and a non included side of the other triangle
The details of the reasons used to prove the ΔABC ≅ ΔCDA are as follows;
Angle sum property of a triangle
The angle sum property of a triangle indicates that the sum of the three interior angles of a triangle is 180°
Reflexive property
Reflexive property of congruency states that a geometric figure is congruent to itself.
ASA congruency rule
The Angle-Side-Angle, ASA, congruency rule states that the if two angles and a non included side of one triangle are congruent to two angles and a non included side of the other triangle, then both triangles are congruent
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how many ways are there to form a committee of 6 people from the department, if the number of men in the committee is less than the number of females in the committee? explain your answer.
there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee by combination.
There are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee. This is because the number of possible combinations of 6 people with varying numbers of men and women is equal to the number of combinations of 6 people with 1 more female than male, plus the number of combinations of 6 people with 1 more male than female (which is equal to the number of combinations of 6 people with 1 more female than male).
Mathematically, this can be expressed as:
Number of combinations = (number of 6-person combinations with 1 more female than male) + (number of 6-person combinations with 1 more male than female)
Number of combinations = (6C4 x 5C2) + (6C5 x 5C1)
Number of combinations = 15
Therefore, there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee.
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Angles 3 and 6 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help!!!
Answer:
A. Same-side interior angles
Step-by-step explanation:
Same-side interior angles are angles that has same-side interior angles sum up to 180 degrees. So, the answer is A.
Answer: A. Same side interior angles
Step-by-step explanation:
because they are inside the parralel lines and they are on the same side of the line going across them
Abdullah and Amna bought a car for $9000. Abdullah paid 45% of the $9000 and Amna paid
the rest.
a) How much did Amna pay towards the cost of the car?
Answer:
$4950
Step-by-step explanation:
100-45 = 55
55% × 9000 = 4950
Kyle uses a calculator to figure out
the total cost of a $1.60 cookie jar.
Including sales tax, the total is
$1.62. What is the sales tax
percentage?
(round your answer to the nearest hundreths)
COOKIES
The sales tax percentage of cookie jar is 1.6% .
What is sales tax?Sales tax is a mandatory fee levied on the purchase of certain goods and services. The cost of goods and services rises as a result of sales tax.(sales tax / total cost of the item) x 100 = sales tax rate
To find the sales tax percentage:
To calculate the tax amount, subtract the net price from the gross price.Subtract the tax amount from the net price.Step 2's result is multiplied by 100. The outcome is the sales tax.Here given,
Total cost = $1.62
Gross price = $1.60
Tax amount = $1.62 - $1.60
= $0.02
By substracting the tax amount from total cost,
$1.62 - $0.02
= $1.6
The sales tax percentage = 1.6%.
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Indicate the domain of each fraction.
a. [tex]\frac{2y}{9+y^{2} }[/tex]
b. [tex]\frac{5x}{3x(x+12)}[/tex]
c. [tex]\frac{7a}{(a+1)(a-4)}[/tex]
Answer: see below
Step-by-step explanation:
The denominator of the equations cannot equal zero.
a. [tex]9+y^{2}[/tex] [tex]= 0[/tex]
[tex]y^{2} = -9[/tex]
[tex]\sqrt{y^{2} } = \sqrt{-9}[/tex]
[tex]y=-3i,3i[/tex]
The domain is all real numbers.
D:xE(−∞,∞)
b.3x(x+12)=0
3x=0, x+12=0
x=0,x=-12
D:xE(−∞.-12) U (-12,0) U (0,∞)
c.(a+1)(a-4)=0
a+1=0, a-4=0
a=1, a=4
D:xE(−∞.1) U (1,4) U (4,∞)
Two-sevenths of the students in the theater club will be in the second show, and three-fifths of them will be in the third show. The rest will be in the first show. If there are 70 students in the theater club, how many of them will be in the first show?
Answer:
8 students
Step-by-step explanation:
Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:
2/7 * x = number of students in the second show3/5 * x = number of students in the third showx - (2/7 * x + 3/5 * x) = number of students in the first showWe are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:
2/7 * 70 = 20 students in the second show3/5 * 70 = 42 students in the third show70 - (2/7 * 70 + 3/5 * 70) = 8 students in the first showTherefore, there will be 8 students in the first show.
Need help solving this
Answer:
No
Step-by-step explanation:
The cost of running six seminars is [tex]10000+1500+6(400+250)=\$15400[/tex].
The revenue earned is about [tex]1500(6)=\$9000[/tex].
Since the revenue is significantly less than the cost, there will not be a profit.
Mariol buy 3 pound of cheee and 3 pound of auage for a total cot of $36. The auage cot $2. 00 le per pound than the cheee. What i the combined cot of 1 pound of cheee and 1 pound of auage?How much would Mariol pay for 4 pound of cheee and 1 pound of auage
Mariol pays $12 for a pound of cheese and a pound of sausage, and $42 for 4 pounds of cheese and 1 pound of sausage.
To solve this problem, we can apply simple algebra. Let's use the letter for the initial, C for a pound of cheese, and S for a pound of sausage.
3 C + 3 S = $36
If the sausage cost $2.00 per pound, so
3 C + 3 ($2) = $36
3 C + $6 = $36
To know the price for a pound of cheese, do as follow
3 C = $36 - $6
3 C = $30
1 C = $30 : 3 = $10
Thus, 1 pound of cheese and 1 pound of sausage would be $2 + $10 = $12
Moreover, if 4C + 1S = 4($10) + 1($2) = $40 + $2= $42
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what is the probability that you reach into the jar and randomly grab a quarter and then, without replacement, a nickel? express your answer as a fraction or a decimal number rounded to four decimal places.
0.688 will be the probability of getting a nickel from the jar.
Given,
Probability;-
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.
Therefore,
P(nickel) = 19/69
P(penny) = 17/68
That is,
P = 19/69 × 17/68
P = 323/4692
P = 0.0688
That is,
The probability of getting nickel from the jar is 0.06888
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a sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. what is the median charge?
The median charge is $51. The median of a data set is also called the middle value.
How to find the median?Median is the value of the middle point in a data set. Here is how to find the median.
Sort the data from the smallest to the biggest.Separate the data into two. If the number of data is odd, the exactly middle part is the median. If the number of data is even, the median is the sum of left and right side divided by two.A sample of the paramedical fees: $55, $49, $50, $45, $52, and $55. Find the median!
The number of the data is 6.
Let's sort the data form the smallest!
$45, $49, $50, $52, $55, $55
The middle part of the data is $50 and $52. The median is
($50 + $52)/2 = $102/2 = $51
Hence, the median of the data is $51.
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Write the equation of the line passing through the points (-4,6) and (4,4).
Answer: y=-(1/4)x+5
Step-by-step explanation:
(-4,6) (4,4)
[tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
x₁=-4 x₂=4 y₁=6 y₂=4
Hence,
[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-6}{4-6} \\\\\frac{x+4}{4+4}=\frac{y-6}{-2} \\\\\frac{x+4}{8} =\frac{y-6}{-2} \\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\-\frac{x+4}{4} =y-6\\\\-\frac{1}{4}x -1=y-6\\\\-\frac{1}{4} x-1+6=y-6+6\\\\-\frac{1}{4} x+5=y\\\\Thus,\ y=-\frac{1}{4} x+5[/tex]
Tom’ mot recent book earned 10*4 time a much money a hi firt book. How much did Tom’ mot recent book earn? Write the amount in tandard form. Explain how you know your anwer i correct. (hint hi firt book earned 10*3)
Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.
How to illustrate the exponent?
The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.
The total amount of the recent book will be:
= 10⁴ × 10³
= 10^(4 + 3)
= 10^7
The amount is 10^7.
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34. Write the equation of each line below.
Answer:
red: y = 3x +2blue: y = 3x -1Step-by-step explanation:
You want the equations of the graphed parallel lines with y-intercepts of 2 and -1, and a rise/run of 3/1.
Slope-intercept equationThe slope-intercept form equation with slope m and y-intercept b is ...
y = mx +b
Each of these lines rises 3 units for each 1 unit to the right, so has a slope of ...
m = rise/run = 3/1 = 3
Red lineThe red line crosses the y-axis at y=2, so its equation is ...
y = 3x +2
Blue lineThe blue line crosses the y-axis at y=-1, so its equation is ...
y = 3x -1
i need help solving!! (x,y)
y = 6x - 3
2x-3y=25
Answer:
Step-by-step explanation:
2x - 3(6x - 3) = 25
2x - 18x + 9 = 25
-16x + 9 = 25
-16x = 16
x = -1
y = 6(-1) - 3 = -6 - 3 = -9
(-1, -9)
find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.
The definite integral of the function f shown in the graph below, over the limits from 0 to 3.
In the given question, we have to find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.
On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as
[tex]\int^{b}_{a}f(x)dx = f(b) - f(a)[/tex]
Any function's definite integral can be written as the upper limit of a sum or, if an anti-derivative F exists for the interval [a, b], as the difference between the values at the points a and b.
[tex]\int^{3}_{0}f(x)dx[/tex] = Area under the curve from 0 to 3
[tex]\int^{3}_{0}f(x)dx[/tex] = 1/2 ×3×12
[tex]\int^{3}_{0}f(x)dx[/tex] = 18
Hence, the definite integral of the function f shown in the graph below, over the limits from 0 to 3 is 18.
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find a so that the two points are 17 units aparts
(-5,8) and (3,a)
please tell me how you found it, i need the help!
Answer:
Therefore, the value of "a" could be 23 or -7 in order for the two points (-5,8) and (3,a) to be 17 units apart.
Step-by-step explanation:
To find the value of "a" such that the two points (-5,8) and (3,a) are 17 units apart, we can use the distance formula to calculate the distance between the two points.
The distance formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for x1, y1, x2, and y2, we get:
distance = sqrt((3 - (-5))^2 + (a - 8)^2)
Simplifying the expression, we get:
distance = sqrt((8)^2 + (a - 8)^2)
distance = sqrt(64 + (a - 8)^2)
Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":
sqrt(64 + (a - 8)^2) = 17
64 + (a - 8)^2 = 289
(a - 8)^2 = 225
a - 8 = 15 or a - 8 = -15
a = 23 or a = -7
Answer: 23 or -7
Step-by-step explanation:
The distance formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for x1, y1, x2, and y2, we get:
distance = sqrt((3 - (-5))^2 + (a - 8)^2)
Simplifying the expression, we get:
distance = sqrt((8)^2 + (a - 8)^2)
distance = sqrt(64 + (a - 8)^2)
Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":
sqrt(64 + (a - 8)^2) = 17
64 + (a - 8)^2 = 289
(a - 8)^2 = 225
a - 8 = 15 or a - 8 = -15
a = 23 or a = -7
find a power series representation for the function. f(x) = x^8 tan^−1(x^3)
The Power series representation of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
What is Maclaurin series?The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.
What is power series?
An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.
The Maclaurin series will be used in this instance to expand the function:
[tex]tan^-^1x[/tex] = [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]
and for [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}[/tex]
=> [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex] -------(i)
and f(x) = [tex]x^8tan^-^1x^3[/tex]
now we need to multiply [tex]x^8[/tex] in the above equation to get the power series expansion of f(x)
[tex]x^8tan^-^1x^3[/tex] = [tex]x^8[/tex] [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]
=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}[/tex]
=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
so the expansion of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]
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I NEED HELP WITH #17
HELP PLEASEE
By complex and real number properties, the resulting electric resistance is equal to R' = 47 / 270 + i 4 / 45 ohms.
How to determine the total resistence of circuit by operation with complex numbers
Complex numbers are numbers of the form z = a + i b, where a, b are real numbers. The first component is the real component and the second one is the complex one. In this problem we find the case of a combination of two electric resistances described by two complex numbers. This expression must be simplified by means of real number and complex number properties:
R' = 1 / R₁ + 1 / R₂
If we know that R₁ = 4 + i 6 and R₂ = 2 - i 4, then the resulting electric resistance is:
1 / (4 + i 6) + 1 / (2 - i 4)
(4 - i 6) / [(4 + i 6) · (4 - i 6)] + (2 + i 4) / [(2 - i 4) · (2 + i 4)]
(4 - i 6) / (16 - i² 36) + (2 + i 4) / (4 - i² 16)
(4 - i 6) / (16 + 36) + (2 + i 4) / (4 + 16)
(4 - i 6) / 52 + (2 + i 4) / 20
(2 - i 3) / 27 + (1 + i 2) / 10
47 / 270 + i 4 / 45
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