We want to find the rate of change of the surface for a cube of increasing volume.
When the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.
We know that for a cube of side length S, the volume is:
V = S^3
And the surface area is:
A = 6*S^2
Here we know that the volume increases at a rate of 12in^3/min.
Because the volume depends on the side length cubed, we can say that the side length increases at a rate of:
∛(12in^3)/min = 2.29 in/min
Then, as a function of time t in minutes, we can write the side length as:
S(t) = (2.29 in/min)*t
Then the surface area equation is:
A(t) = 6*((2.29 in/min)*t)*((2.29 in/min)*t)
A(t) = (31.46 in^2/min^2)*t^2
The rate of change is given by direct differentiation, we get:
A'(t) = 2*(31.46 in^2/min^2)*t
Now we need to evaluate this in the value of t such that the side length is equal to 20 in:
S(t) = 20in = (2.29 in/min)*t
(20in)/(2.29 in/min) = t = 8.73 min
Then we will get:
A'(8.73min) = 2*(31.46 in^2/min^2)*8.73min = 439.29 in^2/min
This means that when the side length is equal to 20 inches, the surface area is increasing at a rate of 439.29 in^2 per minute.
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Eloise rides her bike1 7/10 miles on Wednesday and 1 5/10 miles on Thursday. How many miles does Eloise ride her bike altogether? Enter your answer as a mixed number in the simplest form
Answer:
3 2/10
Step-by-step explanation:
start with an equation:
1 7/10+1 5/10 = ?
convert mixed fractions into improper fractions:
17/10+15/10 = ?
add:
32/10
simplift:
3 2/10
5+55+55+55+55+55+55+55+55+55+55+55+5/0=free
Answer:
Thanks man
Step-by-step explanation:
Answer:
thx
Step-by-step explanation:
What is the application of inverse matrix?
Answer:
The inverse matrix is used to solve the system of linear equations. It also tells us the consistent or inconsistent behaviour of the solution of equations.
Step-by-step explanation:
In real life,
Whereas in programming which is taught at the university, matrices and inverse matrices are used for coding and encrypting messages. Matrices are also used in representing the real world data's like the population of people, infant mortality rate, etc. They are best representation methods for plotting surveys.please help with finding the midpoint
Answer: (-4, -6)
Step-by-step explanation:
Find the middle so find the averages of the x points and the y points
average of -6 and 2 is -4
average of -8 and -4 is -6
the point is (-4, -6)
A quality control engineer inspects a random sample of 3 batteries from each lot of 24 car batteries that is ready to be shipped. If such a lot contains six batteries with slight defects, what is the probability that the inspector's sample will contain none of the batteries with defects
Answer:
10
Step-by-step explanation:
The probability of getting a sample without any defect is 1 / 6.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a quality control engineer inspects a random sample of 3 batteries from each lot of 24 car batteries that are ready to be shipped.
Total batteries = 24
Total non-defective batteries = 24 - 6 = 18
Probability = Number of favourable outcomes / Number of sample
Probability = 3 / 18
Probability = 1 / 6
Therefore, the probability of getting a sample without any defect is 1 / 6.
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OT
The blueprint for Audrey's new room has a
scale that states every inch is actually equal
to 15 inches. If this blueprint shows the length
of her new room to be 3 inches, what will be
the actual length of her new room?
Answer:
I really need points
Good luck with your question tho
prove cos 2 theta - cos 4 theta + cos 6 theta - cos 12 theta = 4 sin 3 theta sin 5 theta cos 4 theta
Answer:
sorry need lng po
Step-by-step explanation:
pa brainlies
The ratio of cups of orange juice concentrate to water in a punch recipe is 3:5. If Connor used 25 cups of water, how many cups of orange juice concentrate did he use
Answer:
15 cups of orange juice
Step-by-step explanation:
Let u be 1 unit.
5u = 25 cups
u = 25÷5
= 5
3u = 5×3
= 15
You are tasked with finding the dimensions of an empty rectangular swimming pool. The goal is to calculate the amount of water needed to fill the pool. What would be the appropriate tool for taking the required measurements?
Please help! will mark brainlest
A. a ruler
B. a protractor
C. a compass
D. a measuring tape
Answer:
Its D
Step-by-step explanation:because the ruler is small and the other tools are not for it porpuse
This question has been answered, thank you so much for trying to help ^^
Ok, but don't spend so much of points it will create a shortages of point for u only, if point will get less then you will not able to ask question anymore.
Got it ^_^
I will ask this question based on the above pic. So I'm picking up a question for this.
Anyways thanks for giving away 26 points to me :))
I'm also asking a question with that amount of points. OK
solve pls brainliest
Answer:
y = 1.28
Step-by-step explanation:
Hi there!
[tex]10.24=8y[/tex]
To solve for y, divide both sides by 8:
[tex]\displaystyle \frac{10.24}{8} =\displaystyle \frac{8y}{8} \\\\1.28=y[/tex]
Therefore, y = 1.28.
I hope this helps!
Answer:
= 1 . 2 8
Step-by-step explanation:
10.24 =8y
10.24 = 8y
8 8
Which of the following coordinates of points belong to the solution set of the inequality y <2x² +3x - 5?
A.(-3,2)
B.(-2,9)
C.(1,6)
D.(3,1)
E. (-1.5)
Answer:
A , DStep-by-step explanation:
Check the inequality for each point.
For A. (-3,2)
[tex]y < {2x}^{2} + 3x - 5 \\ 2 < {2 ( - 3)}^{2} + 3( - 3) - 5 \\ 2 < 2 \times 9 - 9 - 5 \\ 2 < 18 - 9 - 5 \\ 2 < 4 \\ [/tex]
The inequality is satisfied.
For B. (-2,9)
[tex]y < {2x}^{2} + 3x - 5 \\ 9 < 2 {( - 2)}^{2} + 3( - 2) - 5 \\ 9 < 2(4) - 6 - 5 \\ 9 < 8 - 6 - 5 \\ 9 < - 3 \\ [/tex]
The inequality is not satisfied.
For C. (1,6)
[tex]y < {2x}^{2} + 3x - 5 \\ 6 < {2(1)}^{2} + 3(1) - 5 \\ 6 < 2(1) + 3 - 5 \\ 6 < 2 + 3 - 5 \\ 6 < 0[/tex]
The inequality is not satisfied.
For D. (3,1)
[tex]y < {2x}^{2} + 3x - 5 \\ 1 < {2(3)}^{2} + 3(3) - 5 \\ 1 < 2(9) + 9 - 5 \\ 1 < 18 + 9 - 5 \\ 1 < 22 \\ [/tex]
The inequality is satisfied.
For E. (-1,5)
[tex]y < {2x}^{2} + 3x - 5 \\ 5 < {2( - 1)}^{2} + 3( - 1) - 5 \\ 5 < 2(1) - 3 - 5 \\ 5 < 2 - 3 - 5 \\ 5 < - 6 \\ [/tex]
The inequality is not satisfied.
I need help with this please
Answer:
23 isnthe anseeerjfhdhvdvd hdjdbbe
Drag the numbers to order them from least to greatest.
0.7
-4.5
3.0
-0.5
2.3
Answer:
- 4.5, - 0.5, 0.7, 2.3, 3.0
Does any one the the answer
Answer:
18 Square Feet
Step-by-step explanation:
ABC is 3 times larger then DEF so you multiply 6 by 3 which gives you 18. Let me know if I'm wrong.
Answer:
18 square feet
Step-by-step explanation:
Because the area of ADEF =6 sq ft
And you have 12ft in A and B
The length of a marathon race is 26 miles 385 yards. What is the total length of the marathon
race in yards?
Plz help
Answer:
46,145
Step-by-step explanation:
26x1760= 45,760 + 385= 46,145
The total length of the marathon race in yards when the length of a marathon race is 26 miles 385 yards, is 46145 yards.
How to measure the length?Length measurement is the measurement of the size of an object. The units of length measurement are meter, feet, yards etc.
Yards-This unit is used when the size of a small space has to measure, such as length of bed, ladder etc. There are total 1760 yards in one mile.Miles-This is the basic unit of length measurement of size. The size of roads, distance between two cities are measured in miles.The length of a marathon race is 26 miles 385 yards. As there are total 1760 yards in one mile. Thus, the total number of yards in 26 miles is,
[tex]26\times1760=45760[/tex]
Now, he races for 385 yards along with 26 miles. Thus, the length of marathon is,
[tex]45760+385=46145\rm\; yards[/tex]
Thus, the total length of the marathon race in yards when the length of a marathon race is 26 miles 385 yards, is 46145 yards.
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HELP ASAP......find the slope of the line that passes through the two points (-44.42,5.1) and (4.42,4)
Answer:
m ≈ -0.225
Step-by-step explanation:
For points (-44.42, 5.1) and (4.42, 4)
slope = (y2 -y1)/(x2 -x1) = (5.1 -4)/ (-44.42 -4.42) = 1.1 / -48.44 ≈ - 0.225
Suppose a car travels at a rate of 60 miles per hour for 3 hours. How many miles does the car travel?
UPDATE IM DUM IT 180
Answer:
thanks
Step-by-step explanation:
a worker uses 45 inches of steel to make 300 nuts of the same size how many inches of steel wire will be needed to make one such nut?
Answer:
about 6.66666 inches
Step-by-step explanation:
It says you're in college why do you need help with such a simple problem?
9. plsss help, will give brianlist
Answer:
[tex]1. \: \: \: \: \frac{1}{5} \\ 2. \: \: \: \: - \frac{3}{2} \\ 3. \: \: \: \: \frac{1}{2} [/tex]
Step-by-step explanation:
1. In the first diagram we simply count the number of squares along the rise and the number of squares along the run as slope equals rise/run
2. we use the slope formula
[tex] \frac{y2 - y1}{x2 - x1} = \frac{ - 2 - 1}{ 1- ( - 1)} = \frac{ - 3}{2} = - \frac{3}{2} [/tex]
3. pick any two points and apply the slope formula again
[tex]( - 1. \: \: 1) \: and \: (3. \: \: 3) \\ \frac{3 - 1}{3 - ( - 1)} = \frac{2}{4} = \frac{1}{2} [/tex]
x likes teenager but hates children, x likes running but hates walking, x likes swimming but hates water, x likes trees but hates flowers, x likes jeeps but hates car, x likes beef but hates pork. from the following what does x likes?
Step-by-step explanation:
x likes teenagers, running, swimming , trees , jeeps and beef.
[(-2)²×3]÷[(-9)-5+2]
Answer:
-1
Step-by-step explanation:
1. To simplify this expression, let's go through the steps of BODMAS.
[tex]\frac{(-2)^2(3)}{-9-5+2}[/tex] [tex]\frac{(4)(3)}{-9-5+2}[/tex] [tex]\frac{12}{-9-5+2}[/tex] [tex]\frac{12}{-14+2}[/tex] [tex]\frac{12}{-12}[/tex] [tex]-1[/tex]Therefore, the answer is -1.
Help please i just wanna pass
I'll give Brainliest, I need this now. :D
Answer:
I think it's 6:3=18:9=54:27
Step-by-step explanation:
I hope this helps!
Find the missing value so that the line passing through the points has the given slope.
(7,1) and (x,4); m = 3/4
Answer:
11
Step-by-step explanation:
4-1=3/11-7=4
Please answer this question
Answer:
See explanation below:
see attached file below
What is the coefficient of 5(-t)
HELPPP
Answer:
-5
Step-by-step explanation:
Here are the steps to take in calculating the correlation coefficient:
Determine your data sets.
Calculate the standardized value for your x variables.
Calculate the standardized value for your y variables.
Multiply and find the sum.
Divide the sum and determine the correlation coefficient.
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
2b ^ 3 + 2
Answer:
There are no like terms.
Step-by-step explanation:
Answer: if i remember correctly you’re just supposed to add 2 to the exponent so it’s be 2b^5 if that’s not the case then there are no like terms
Step-by-step explanation:
What do you already know about credit cards?
Answer:
A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Step-by-step explanation:
Check all solutions to the equation. If there are no solutions, check "None."
x = 16
Someone please help!!
Answer:
Its E
Step-by-step explanation: