Answers
Answer:
First is option B)
Second is option B)
I hope my answer helps you.
Related Questions
Write the following inequality in slope-intercept form.
5x - y > -14
Answers
Answer:
y > 5x + 14
Step-by-step explanation:
5x – y > –14
–y > –5x–14
divide both sides by (–)
–(–y) > –(–5x–14)
y > 5x + 14
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Ralf and Susie share$57 in the ratio 2:1.Calculate the amount Ralf rec
eive
Answers
Step-by-step explanation:
since the fraction is a ratio, we know that the whole amount of $57 consists of 2+1 = 3 equally sized parts.
Ralf gets 2 of these parts, Susie one part.
each part is
57 / 3 = $19
so, Ralf gets
19×2 = $38
Susie gets
19×1 = $19
refer to exhibit 1-3. based on the data provided in this table, what type of relationship exists between variables x and y?
Answers
Based on the data provided in the table, an inverse relationship exists between variables x and y. (Option A)
An inverse relationship refers to a relationship between two variables that changes in opposite directions. In other words, an increase in one variable results in a decrease in the other variable and vice versa. An inverse relationship is represented in the form of y = k/x, where x and y are two variables and k is the constant value. Based on the data provided in the table, as the value of x increases, the value of y decreases by a constant value. Hence, the relationship that exists between variable x and y is inverse.
Note: The question is incomplete as it is missing options which are A) inverse B) direct C) independent d) there is no relationship between variable x and y.
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Nicole has saved $120 toward the purchase of a new bike. She gets a job that pays $12 an hour. She saves 25% of her hourly wage to purchase the new bike. She uses the equation y=(0.25)(12)x+ 120 to determine how much money she has saved toward the purchase of the new bike. What is the slope of the line represented by Nicole's equation?
A. 120
B. 0.25
C. 12
D. 3
Answers
Answer: The correct answer is B.
Step-by-step explanation:
The slope of a line in the form of y = mx + b is represented by the coefficient m. In this case, the slope of the line represented by Nicole's equation is:
y = (0.25)(12)x + 120
The coefficient m is 0.25.
A farmer needs to construct twO adjoining rectangular pens of identical areas (15 points) showa in the figure below . If each pen is to have an area of 1200 square feet, what dimeosions will minimize the length of fencing? 1200 sq: ft. 1200 sq. ft,
Answers
A farmer needs to construct two adjoining rectangular pens with each pen is to have an area of 1200 square feet. So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.
Determine dimeosions will minimize the length of fencingFor pictures of two rectangular pens, see the attachment.
Area of rectangle = length × width
A = x × y
1200 = xy
y = 1200/x
The entire length of the fence
P = 3x + 4y
P = 3x + 4 (1200/x)
P = 3x + 4800/x
P = 3x + 4800x⁻¹
Find dimentions will minimize the length of fencing, if P' = 0.
P = 3x + 4800x⁻¹
P' = 3 - 1 × 4800x⁻¹⁻¹
0 = 3 - 4800x⁻²
4800x⁻² = 3
4800/x² = 3
4800 = 3x²
x² = 4800/3
x² = 1600
x = 40
y = 1200/x
y = 1200/40
y = 30
So dimeosions will minimize the length of fencing is length = 40 ft and width = 30 ft.
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Let A be a square matrix. Assume that the following statement is true: If B is an invertible matrix then rank BA = rank A. (a) Show that if B is an invertible matrix then rank AB = rank A. Hint: What is rank(AB)" ? (b) Show that for any invertible matrix P, rank(P-'AP) = rank A. (c) If P is invertible then nullity P-'AP = nullity A.
Answers
We proved the expression rank(AB)=rank(B) and rank(BA)=rank(B),
where A and B are the two matrices of same order.
Given, A is a square matrix.
If A is invertible and a n×n square matrix of full rank.
Since both AB and BA exist, where B is also a n×n square matrix.
rank(B)=rank(BT)
On using the rank–nullity theorem, we get
nullity of a matrix be n minus the rank of the matrix.
So let U be a matrix whose columns are a basis for the nullspace of AB, so that ABU = 0.
Pre-multiplying both sides by A−1 , we obtain BU=0,
As B and AB have the same rank.
Similarly, let V be a matrix whose columns are a basis for the null space of ATBT, so that ATBTV=0 .
Pre-multiplying both sides by (A−1)T , we get
BTV=0.
Since rank(BT)=rank(B) and rank(ATBT)=rank((BA)T)=rank(BA)
we get rank(AB)=rank(B) and rank(BA)=rank(B).
So, rank(AB)=rank(B) and rank(BA)=rank(B).
Hence, rank(AB)=rank(B) and rank(BA)=rank(B).
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The price of desktop computer decrease from 3160 to 1020 find the percentage
Answers
Answer:
67.7215189873%
Step-by-step explanation:
The price of a desktop computer decreases from $3160 to $1020
Initial price of desktop =$3160
New Price= $1020
Change in price = 3160 - 1020 = 2140
Percentage decrease = [tex]\frac{2140}{3160}[/tex][tex]X[/tex][tex]100[/tex]=67.7215189873%
Hence , the answer is 67.7215189873%
Hope it helps u
reported the results of a study on the occurrence of sodium and chloride in surface streams in central rhode island. the following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).
Answers
The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases.
| Roadway Area (x) | Chloride Concentration (y) |
|--------------------|--------------------------|
| 10.7 | 28.2 |
| 11.3 | 28.3 |
| 11.7 | 28.4 |
| 11.8 | 28.5 |
| 12.6 | 28.8 |
| 13.2 | 29.2 |
The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases. Specifically, there was a statistically significant positive correlation between the two variables, with the chloride concentration increasing by an average of 0.3 mg/L for every 1% increase in the roadway area in the watershed.
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Select all the equations that are NOT equivalent to p – 7 = 22.
Answers
Answer:
I'm sorry but this question isnt do-able without the multiplechoice
Step-by-step explanation:
Round 23.492 the nearest hundredth
Answers
Answer: 23.49
Step-by-step explanation:
Look at the thousandths place and the hundredths place.
92
Now we round 92.
1-4 it stays the same
5 or more you raise it
92 is about 90.
So you would get 23.490
You can eliminate the excess zero.
Your answer is 23.49
explain how to use the multiplication table to solve 5 x 4
Answers
Answer:
Go and look up your tables and read below
Step-by-step explanation:
To solve the problem 5 x 4 using the multiplication table, you would look up the corresponding entries in the table for the numbers 5 and 4. In the row labeled 5 and the column labeled 4, you would find the product 20, which is the answer to the problem 5 x 4.
answer
Step-by-step explanation:
christopher is working two summer jobs, making $7 per hour babysitting and making $10 per hour washing cars. in a given week, he can work no more than 16 total hours and must earn a minimum of $130. if xx represents the number of hours babysitting and yy represents the number of hours washing cars, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Christopher can work average 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Christopher is working two summer jobs and has a maximum of 16 hours to work in a given week. He is making $7 per hour babysitting and $10 per hour washing cars. To meet the minimum wage requirement of $130, he needs to make a total of $130 in a week. We can represent this using a system of inequalities. The first inequality is 7xx + 10yy ≥ 130, which means that the total wages (7 times the hours babysitting plus 10 times the hours washing cars) must be greater than or equal to $130. The second inequality is xx + yy ≤ 16, which means that the total hours (babysitting plus washing cars) must be less than or equal to 16. Graphically, we can solve this system of inequalities to find the possible solutions. One possible solution is x = 9 and y = 7, meaning Christopher can work 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Graphically:
7xx + 10yy ≥ 130
xx + yy ≤ 16
7xx + 10yy = 130
xx + yy = 16
Therefore, the solution is x = 9 and y = 7.
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To find the length of the diagonal from point A (front/bottom/left) to point G(back/top/right):
You would first use on the bottom of the box rectangle to find the diagonal AC=
Then use CG as of the triangle ACG, with AG being the
AG is approximately =
Word Bank:
square root 73 cm the Pythagorean Theorem the area formula for a rectangle 11 cm the hypotenuse
the perimeter formula for a rectangle 9.4cm a leg 3cm square root 11cm 73 cm 89 cm
Blank 1:
Blank 2:
Blank 3 :
Blank 4:
Blank 5:
Answers
The length of the diagonal from point A to point G is √89.
Blank 1: Using the Pythagorean Theorem
Blank 2: Finding the AC.
Blank 3: Now use CG as a adjacent side.
Blank 4: Now AG is being Hypotenuse.
Blank 5: Now find AG.
In the given question, we have to find the length of the diagonal from point A to point G.
We would first use on the bottom of the box rectangle to find the diagonal AC.
Then we use CG as of the triangle ACG.
Blank 1: Using the Pythagorean Theorem
In this theorem; a^2+b^2=c^2
Where a=adjacent side, b=base, c=hypotenuse
Blank 2: Finding the AC.
Now in the triangle ABC, use Pythagorean Theorem
So AC = √(AB)^2+(BC)^2
AC = √(8)^2+(3)^2
AC = √64+9
AC = √73
Blank 3: Now use CG as a adjacent side.
Blank 4: Now AG is being Hypotenuse.
Blank 5: Now find AG.
Now in the triangle ACG, use Pythagorean Theorem
So AG = √(AC)^2+(CG)^2
AG = √(√73)^2+(4)^2
AG = √73+16
AG = √89
Hence, the length of the diagonal from point A to point G is √89.
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the sampling distribution of the sample mean is close to normal distribution a. only if the parent population is unimodal, not badly skewed, and does not have outliers.
Answers
C) The Central Limit Theorem states that the sample mean's sampling distribution is very similar to a normal distribution.
The central limit theorem is founded on what?The idea of a sampling distribution, which is the probability distribution of a statistic for a large number of samples taken from a population, is the foundation of the central limit theorem.
What are the central limit theorem's two main tenets?To summarize, the following two distributions are linked by the central limit theorem: The population's distribution of the variable. The testing dissemination of the mean.
What is As far as possible Hypothesis?The CLT is a statistical theory that holds that the mean of all samples taken from a population with a finite level of variance will roughly match the population mean if a sufficient number of samples are taken from that population.
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Full Question = The sampling distribution of the sample mean is close to the normal distribution
A. only if the parent population is unimodal, not badly skewed, and does not have outliers.
B. no matter what the distribution of the parent population of what the value of n.
C. if n is large, no matter what the distribution of the parent population.
D. if the standard deviation of the parent population is known.
E. only if both n is large and parent population has a normal distribution.
find $m\angle1$ .two triangles a b c and q r s are drawn. angles b and q are labeled with a single arc. angles a and s are marked with a double arc. angles a and b are labeled 45 degrees and 80 degrees respectively. angle r is labeled 1.
Answers
The measure of angle 1, m∠1, found using the congruency of the angles and the angle sum property of a triangle is 55°
What is the angle sum property of a triangle?The angle sum property of a triangle specifies that the sum of the interior angles of a triangle is 180°
Please find attached the presentation of the details of the question as a drawing of the triangles created with MS Word
The parameters of the question are;
The number of arcs on angles b and q = Single arcs
Therefore, based on the arc markings indicating congruency of the angles, we get;
Angle b is congruent to angle q ∠b ≅ ∠q
Therefore, ∠b = ∠q, by the definition of congruency
The number of arcs on angle a and angle s = Double arcs
Therefore, angle a is congruent to angle s based on the arc markings, which indicates;
∠a ≅ ∠s
∠a = ∠s by the definition of congruency
The label on angle ∠a = 45°
The label on angle ∠b = 80°
∠a = ∠s, therefore, ∠s = 45°, by substitution property
∠b = ∠q, therefore, ∠q = 80° by substitution
∠s + ∠q + ∠1 = 180° Angle sum property of a triangle
45° + 80° + m∠1 = 180°
m∠1 = 180° - (45° + 80°) = 55°
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WILL GIVE BRAINLIST! The story is "I, Too, Have a Dream" by Brittany Taylor.
Directions: Use your planning in Part 1 to write your two body paragraphs in the box below. The box will expand. Use complete sentences, proper grammar and punctuation, and transitions to develop your body paragraphs. Each body paragraph should have a transition at the beginning of the topic sentence and at least two within each paragraph.
Body paragraph 1: Topic Sentence: Brittany Taylor states people's dream to keep DACA up, so the editor can let DACA stay in the U.S.
Example from text to support topic sentence: “Yes, Areliss is a DREAMer. But I, too, have a dream. My dream is that DACA will be reinstated. My dream is that Areliss will be invited to stay in the country she was born in and live out her dreams in the country she loves.”
Explanation of how the example serves purpose: Brittany states that she has a dream to keep the DACA in the U.S. so that her befriend, Areliss can stay to live her dreams and stay in the country as well.
Example from text to support topic sentence: “DACA recipients have a dream: they dream that their lifelong contribution to the United States will one day be recognized, and they will be permitted to stay in the country they have always called home.”
Explanation of how the example serves purpose: Brittany is trying to convince the editor that DACA has a dream to be recognized and stay around and not get shut down.
Body paragraph 2:
Topic Sentence: Brittany Taylor uses figurative language such as metaphors and similies to tell the audience why DACA should be reinstated.
Example from text to support topic sentence: “But, I know their words were bullets to Areliss’s heart.”
Explanation of how the example serves purpose: She uses a metaphor in the sentence to show how she knew her best friend felt when the protesters were saying awful things.
Example from text to support topic sentence: “These protesters couldn’t have known what Areliss felt as they shouted and waved pamphlets in our faces like tattered flags.”
Explanation of how the example serves purpose: She uses simile in the sentence to show how hard and rudely they were waving the pamphlets in their faces as if it was a ripped flag.
Answers
Brittany Taylor employs some figurative language in her letter to the editor titled "I, Too, Have a Dream." She employed personification and metaphors. In order to persuade her audience to support the reinstatement of DACA, she makes her ideas by presenting a problem and a solution. According to Brittany Taylor's letter, she used personal experience and official government documents like the DACA to prove that deportation is cruel.
What was the literary work about?Brittany Taylor expresses the desire for DACA to continue so that the editor will permit its continuation in the United States. In order for her friend Areliss to continue living her dreams and remaining in the country, Brittany says she has a dream to keep DACA in the United States.
DACA recipients have a dream: they hope that one day their lifetime of service to the US will be acknowledged and they will be able to remain in the place they have always called home. An explanation of how the example achieves its objectives Brittany is attempting to persuade the editor that DACA has a dream to be acknowledged, remain operational, and not be terminated.
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Answer:
An idea to help: In “I, Too, Have A Dream”, Brittany Taylor, the author, uses a metaphor to help emphasize an objective in the minds of the audience
U KICKED ME OUT HOPE THIS HELPS KATEEEEE!
Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.
What is rewrite?
The term rewrite sentence refers to the sentence was the written in the sentence but in the different style. It was to describe the sentence meaning was the similar, but the wittering style was the different. The rewrite the sentence was the but not the copy to the sentence.
According to the given, the sentence are the rewrite. There was the sentence is the different but, the meaning was the same. The sentence was the "Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind."
As a result, the sentence was the Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.
one period of a sine function or cosine function is called one amplitude incorrect: your answer is incorrect. of the sine curve or cosine curve.
Answers
The correct answer is cycle. A sine or a cosine function represent periodic functions where the value of the function is repeats after a definite interval.
What do you mean by periodic function?
A periodic function can be defined as:
A function returning to the same value at regular intervals. Though periodic motion and oscillatory motion sound the same, not all periodic motions will be oscillatory motion.
Image result for periodic function
If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern.
A motion that repeats itself at regular intervals is termed periodic motion. 1. A motion that does not repeat itself at regular intervals is termed non-periodic motion. 2. After a certain period of time, an object exhibiting periodic motion returns to its original position.
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Read the following prompt and type your response in the space provided.
The perimeter of Dawna's new flat screen television is 70 inches. The ratio of its length to width is 4:3. Write and solve an algebraic equation to determine the dimensions of the television.
Answers
Answer:4*3+70=840
Step-by-step explanation:
Perimeter = 2(Length + Width)
length = 4x ; width = 3x ; perimeter = 70
SOLUTION:Perimeter = 2(Length + Width)
70 = 2(4x + 3x)
70 = 2(7x)
70 = 14x
x = 5
Length = 4x = 4(5) = 20 inchesWidth = 3x = 3(5) = 15 inchesCHECKING:Perimeter = 2(Length + Width)
70 = 2(20 + 15)
70 = 2(35)
70 = 70
We proved and checked the answer.Therefore, the length of the screen television is 20 inches while the width is 15 inches.CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
A chemical plant manufactures fertilizer. A particular fertilizer recipe calls for 2 units of potash for every 3 units of urea. The potash is shipped to the plant in modular pallets with dimensions (x+6) by (x-2). The urea is shipped to the plant in modular pallets with dimension (x-2) by (x+1). Assuming equal molar density in each product, calculate x such that there is no material left over after manufacturing the fertilizer.
Answers
The value of x such that no meterial left over after manufacturing the fertilizer is 1
How to calculate for x?The area of a place is the floor space occupied by an object. we are to determine the value of x in the length and width of the floor to be used by the manufacturer
The givn parameters are the use of
2 units of potash and
3 units of urea.
Recall that the area of a rectangular floor space is (L*W).
This implies that (x+6)(x-2)=2
x²-2x+6x-12=2
x²+4x-10=0 .......................... (1)
Also, for the urea
Area= (x-3)(x+1)=3
x²+x-2x-2=3
x²-x-2-3=0
This implies that
x²-x-5=0 .............................(2)
Assuming equal molar density in each product,
equations 1 and 2 are equal
x²+4x-10=x²-x-5
Collecting like terms
x²-x+4x+x-10+5=0
5x-5=0
5x=5
x=1
Therefore, assuming equal molar density in each product the value of x=1
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the diagrqam shows an object with a mass of 1.0 kiolgram attached to a string 0.50 merer long. the object is moving at a constant speed of 5.0 meters per second in hporizontal circular path with center at point o
Answers
The object is undergoing uniform circular motion. The radius of the circular path is equal to 0.50 meters. The centripetal force, F, acting on the object can be calculated using the equation F= mv^2/r in hporizontal circular path
m is the mass of the object, v is the velocity of the object and r is the radius of the circular path.
F = (1.0 kg) (5.0 m/s)^2 / 0.50 m
F = 50.0 kg m/s^2
The object is undergoing uniform circular motion, which means it is moving at a constant speed in a circular path with its center at point O. The radius of the circular path is equal to 0.50 meters. The force acting on the object is known as the centripetal force, and can be calculated by using the equation F= mv^2/r. This equation requires the mass of the object (m), its velocity (v), and the radius of the circular path (r). In this case, the mass is 1.0 kg, the velocity is 5.0 m/s, and the radius is 0.50 m. Plugging these values into the equation gives the centripetal force acting on the object as 50.0 kg m/s^2.
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what is the square root of 81
Answers
Answer: I hope this is helpful
Step-by-step explanation:
The square root of 81 is 9 and you can say -9
We can find the square root of 81 using prime factorization method, or repeated subtraction method.
81 is a perfect square number and it is the fourth power of 3. we will calculate the square root of 81 by repeated subtraction method and solve a few interesting problems.Square Root of 81: √81 = 9
The square root of a number is the number that when multiplied to itself gives the original number as the product. Finding the square root of a number is the inverse of squaring a number. 81 = a × a = a2 Thus, a = √81= √(9 × 9)9 × 9 = 81 or -9 × -9 = 81. Therefore √81= ± 9This shows that 81 is a perfect square.
¿Do you think that Mexico is transitioning to a green economy? why?
Answers
Answer:
Step-by-step explanation:
yes probaly
im doing this for point
Personally, he considered that Mexico is indeed transitioning to a green economy, because the economy is adjusting towards the sustainable and adequate use of resources.
¿What is the green economy?It is a type of economy that is based on developing sustainable and sustainable processes in all its processes and activities, this in favor of caring for the planet and its natural elements.
¿Does Mexico seek to have a green economy?It can be said that Mexico is transitioning to a green economy, this can be observed, for example:
In the implementation of sustainable and sustainable strategies of companies.In the appropriate and increasingly efficient use of many natural resources.¡Hope this helped!
a manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. the distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. a random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. test at the 10% significance level the null hypothesis that the population mean weight is at least 16 ounces.
Answers
As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.
What is standard deviation ?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.
The following null and alternative hypotheses need to be tested
H0 : µ = 16
Hα : µ < 16
This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28
The rejection region for this left-tailed test is R = {z : z < -1.282}
The z-statistics is computed as follow
[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]
= (15.84 - 16) / (0.4 / √16)
= -1.6
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A 6.05 percent coupon bond with 20 years left to maturity is offered for sale at $1,075.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) (Round your answer to 2 decimal places.)
Answers
Answer:
TVM calculator: N = 40, PV = -1,075.25, PMT = 30.25, FV = 1,000; CPT I = 2.714% YTM = 2.714% × 2 = 5.43%
Step-by-step explanation:
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
Answers
The value of the other points in each of the number line is;
a) M = -2¹/₂; N = -1; R = 4
b) M = -1; P = 1; R = 1.6
c) M = -125; P = 125; N = -50
d) N = -6; P = 15; R = 24
How to interpret Number Lines?a) The point P = 2¹/₂
The distance from point 0 of the number line to point P is 5 units and therefore;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) The point N = -0.4
The distance from point 0 of the number line to point N is 2 units and therefore;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) The point R = 200
The distance from point 0 of the number line to point R is 8 units and therefore;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) The point M = -15
The distance from point 0 of the number line to point N is 5 units and therefore;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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find the least positive integer $n$ such that the set of $1000$ consecutive integers beginning with $1000\cdot n$ contains no square of an integer.
Answers
The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.
3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.
Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282
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problem 9-6 determine the distance yc to the center of gravity of the homogeneous rod bent into the parabolic shape. given: a
Answers
Step 1
We are given a homogenous rod in a cubic curve shape having two free ends, upper end B
and lower end x
The distance of the upper end from x
axis is 1m
and from y axis is 2m.
The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by
[tex]y=2 x^3[/tex]
Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.
Step 3
The given equation of the homogenous rod is,
[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]
The given equation of the homogenous rod is,
\begin{aligned}
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]
[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]
[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]
Substituting the values in the above expression and solving,
[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]
Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,
[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]
Therefore, the center of gravity of the given homogeneous rod is
0.857 m above the horizontal axis
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Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 8) point (−2, −1)
f(x) =?
Answers
Answer:
y=-7(x+1)^2 +8
Step-by-step explanation:
Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.
y=-9(x+1)^2+8
start with the vertex form of a parabola:
y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.
1. plug in the vertex coordinates
y=a(x+1)^2+8
2. to find "a", plug in the point coordinates in the function from step 1 for x and y
-1=a(-2+1)^2+8
when you solve this equation, you will find that a=-9
3. substitute "a" value in the equation from step 1
Done
Use inductive reasoning to predict the most probable next number in the list.
8, 15, 1, 8, −6, 1, −13, −6, −20, ?
Answers
Answer:
-13
Step-by-step explanation:
the pattern goes +7 - 14, so -20 + 7 = 13
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. the possible outcomes of the sample space s are listed as follows, where in each case the die on the left is blue and the one on the right is gray. s = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or o for the empty set.) The event that the sum of the numbers showing face up is at least 9. E Compute its probability.
Answers
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36
The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.
To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.
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