Given:
All the edges of a cube are expanding at a rate of 4 in. per second.
To find:
The rate of change in volume when each edge is 10 in. long.
Solution:
Let a be the edge of the cube.
According to the question, we get
[tex]\dfrac{da}{dt}=4\text{ in./sec}[/tex]
[tex]a=10\text{ in.}[/tex]
We know that, volume of a cube is
[tex]V=a^3[/tex]
Differentiate with respect to t.
[tex]\dfrac{dV}{dt}=\dfrac{d}{dt}a^3[/tex]
[tex]\dfrac{dV}{dt}=(3a^2)\times \dfrac{da}{dt}[/tex]
Putting the given values, we get
[tex]\dfrac{dV}{dt}=(3(10)^2)\times 4[/tex]
[tex]\dfrac{dV}{dt}=3(100)\times 4[/tex]
[tex]\dfrac{dV}{dt}=300\times 4[/tex]
[tex]\dfrac{dV}{dt}=1200\text{ in}^3\text{/sec}[/tex]
Therefore, the rate of change in volume 1200 cubic inches per second.
help for a. a b on my gade who can do it
Answer:
need more information and I can help you
Step-by-step explanation:
If you want me to help please give me more information on what I need to do for you.
Answer:
a
Step-by-step explanation:
Which point is located at -3/2
Answer:
point B
Step-by-step explanation:
it turns in to -1 1/2
Answer:
b
Step-by-step explanation:
A recipe says to use 3 cups of flour to make 48 cookies. How many cups of flour do you need to make 32 cookies?
read and solve each problem learning task 2 page 23 week 5 and learning task 3
eden bought 2 1/4 meter of cloth. She uses 3/4 of meter for her project.how many meters of cloth did she have left
Rina bought 51/4 meter of cloth. She uses 3 3/4 of meter for her project.how many meter of cloth dis she have left
Answer:
1 1/4
1 1/2
Step-by-step explanation:
Given that :
Length of cloth purchased = 2 1/4
Length used for project = 3/4
Length remaining = (length purchased - length used)
= 2 1/4 - 3/4
= (9/4 - 3/4)
= (9 - 4) / 4
= 5/4
= 1 1/4
Length of cloth purchased = 5 1/4
Length used for project = 3 3/4
Length remaining = (length purchased - length used)
= 5 1/4 - 3 3/4
= 21/4 - 15/4
= (21 - 15) / 4
= 6/4
= 1 2/4
= 1 1/2
Susan's elevation at the top of a mountain is 1,530 meters. After 4 hours of climbing down her elevation is 680 meters. What is Susan’s average change in elevation, in meters per hour
A) -850
B)-382.50
C) -212.5
D) -167.5
Rate of a quantity is always in comparison to some other quantity's change. Susan’s average change in elevation, in meters per hour is given by: Option C) -212.5 meters/ hour.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
(its final value - initial value for both dependent and independent variable).
The average change in elevation in meters per hour is ratio of change in elevation in meters to time taken to do it in hours.
Therefore, it is calculated as:
[tex]A = \dfrac{ 680 - 1530}{4} = \dfrac{-850}{4} = -212.5 \: \rm meters/hour[/tex]
(if t was initial time, and t+4 was final time, then t+4-t = 4)
(also, initial height was 1530
Thus, Susan’s average change in elevation, in meters per hour is given by: Option C) -212.5 meters/ hour
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Let v = ⟨-5, 12⟩. What is the approximate direction angle of v?
- 23
- 67
- 113
-157
All options are in degrees
Answer:
c 113
Step-by-step explanation:
The required direction angle of v is 113°. Option C is correct.
v = ⟨-5, 12⟩
Direction angle for v to be determine.
Direction angle define as the vector projected direction.
Here,
Direction angle,
[tex]\alpha =tan^{-1}\frac{12}{-5}\\\alpha = -67.38[/tex]
Now,
[tex]\theta = 180 + \alpha \\\theta = 180+(-67.38)\\\theta = 113[/tex]
Thus, the required direction angle of v is 113°.
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I NEED HELP WITH THIS QUESTION I DONT UNDERSTAND
Answer:
multiply
Step-by-step explanation:
0.54*3100= 1674 students are female
A camp counselor has $53.27 in a bank account and earns an additional $452.68 over summer vacation. The camp counselor spends $193.00 on clothes and wants to buy a plane ticket for $298.11.
I NEED HELP ASAP EXPLAIN THINKING
Answer:
First you do, $53.27+$452.68=$505.95
Next you do, $193+$298.11=$491.11
Last you do, $505.95-$491.11=$14.84
So in the end, the camp counselor will have $14.84 left.
Step-by-step explanation:
Hope that helps! :)
If x^2+y^2=1, what is the largest possible value of |x|+|y|?
If x² + y² = 1, then y = ±√(1 - x²).
Let f(x) = |x| + |±√(1 - x²)| = |x| + √(1 - x²).
If x < 0, we have |x| = -x ; otherwise, if x ≥ 0, then |x| = x.
• Case 1: suppose x < 0. Then
f(x) = -x + √(1 - x²)
f'(x) = -1 - x/√(1 - x²) = 0 → x = -1/√2 → y = ±1/√2
• Case 2: suppose x ≥ 0. Then
f(x) = x + √(1 - x²)
f'(x) = 1 - x/√(1 - x²) = 0 → x = 1/√2 → y = ±1/√2
In either case, |x| = |y| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
An equation is formed of two equal expressions. The largest possible value of |x|+|y|=1.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the value of x²+y²=1. Therefore, The largest possible value of |x|+|y|=1.
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Please it’s due today I need help ASAP
Identify the pairs of alternate exterior angles in the given figure.
Question 14 options:
A)
∠3 and ∠6; ∠4 and ∠5
B)
∠2 and ∠7; ∠1 and ∠8
C)
∠3 and ∠5; ∠4 and ∠6
D)
∠1 and ∠7; ∠2 and ∠8
Answer: Choice D
Angle 1 and angle 7Angle 2 and angle 8=========================================================
Explanation:
The angles 3,4,5,6 are all considered interior angles because they are inside or between the parallel lines.
The remaining angles 1,2,7,8 are exterior angles as they outside the parallel lines. You can think of angles 3,4,5,6 being in the river or a road, while the other angles are on the sidewalk or the shoreline.
Alternating angles are ones that are on either side of the transversal cut.
Combining the two ideas leads to alternate exterior angles being outside the parallel lines and on either side of the transversal. This applies to the following pairs:
angle 1 and angle 7angle 2 and angle 8This is why choice D is the answer.
5. Factor: x² - 4x-21
Answer:
(x - 7) (x + 3)
Step-by-step explanation:
A six-sided die is rolled at the same time as a coin is flipped
a. Are the events independent or dependent?
b. What is the probability of rolling a 4, 5, or 6 AND getting “tails" ?
Answer:
A. Independent
B. 50%
Step-by-step explanation:
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day,
306 people entered the park, and the admission fees collected totaled 784.00 dollars. How many
adults were admitted?
O 176
O 130
O 196
HELP ASAP IM BEING TIMED!!!!!
What rational number represents -10,000?
Decline of 11.3%
I have to identify it as a growth or decay and then write it in decimal form
Answer:
decay.
Step-by-step explanation:
decline means reduce, which is a negative term. decay is also negative.
decimal form= .113 or .11
HELP PLS ASAPPPPPPPPPPPPPP
Answer: Wouldn't the answer be A?
Step-by-step explanation:
Evaluate 62 – (9+ 2) when x = 3.
O A. 12
B. 33
C. 9
D. 27
Answer:
where is the x supposed to be?
Step-by-step explanation:
An inference _______.
a. is a possible explanation for events using prior knowledge
b. explains if a hypothesis is or is not valid
c. is made independent of observation or prior knowledge
d. can be either qualitative or quantitative
Answer:
It is a possible explanation of events using prior knowledge
Step-by-step explanation:
What numbers would be in the in the 4 sections of a 2 x 2 array that shows the problem 19 x 11?
100, 100, 90, 9
100, 10, 90, 9
100, 90, 10, 1
10, 10, 9, 9
Answer:
100, 90, 10, 1
Step-by-step explanation:
pls help ill give brainliest
Jose used a total of 2 5/6 gallons of gas while driving his car. Each hour he was driving, he used 3/10 gallons of gas. What was the total number of hours he was driving?
Answer:
19 hours
Step-by-step explanation:
2.83333/.3= 19.44
Hypatia has read 20 chapters of a 22-chapter book. What percent of the chapters has she read?
Answer:
90%
Step-by-step explanation:
Generate and solve another division problem with the same quotient and remainder as the two problems below.explain your strategy for creating the new problem
Answer:
ITS AN ASSESMENT THIS VIOLATES THE HONOR CODE
Step-by-step explanation:
Answer:
153/47
Step-by-step explanation:
if you plug any number into x you get a valid soultion
(3x+12)/x
If you help on this question you will get brainlest and points !
Answer:
C. 6x+100<150
Step-by-step explanation:
Because yyour putting the two items together but they can't be more than 150
Cassie earned $238 last week when she worked 28 hours. If her weekly earnings are directly proportional to her hours worked, how much will she earn if she works 39 hours next week?
Answer:Commission
An amount of money paid for selling a product or service
Commission Rate
A specified amount of money paid for each sale or a percent of the total value of sales
Step-by-step explanation:
Commission
An amount of money paid for selling a product or service
Commission Rate
A specified amount of money paid for each sale or a percent of the total value of sales
Georgia had 18 cookies. She wanted to split these cookies up evenly among 3 friends and still have at least 1 cookie left over for her. Which of the following amounts of cookies could Georgia give to each of her friends? Select three that apply.
A
5
B
515
C
512
D
545
E
6
F
613
What is 850 in scientific notation?
Answer:
it is 8.5 x 10^2 because when you times the 10 twice and then multiply it with 8.5 and the decimal moves
put the sides in smallest to greatest! will give brainliest
Answer:
bc, ab, ac
Step-by-step explanation:
if it takes a leopard to run 500 yards in 1/2 a min how how many miles could it run in 2 hours
Answer:120000
Step-by-step explanation:
bc in a minute their is 60 seconds and if the leoperd runs 500 yards every 30 seconds u would multiply 60 times 2 bc their is 60 min in a hour and u would get 120.then u would multiply that by 2 getting u 240 which is two hours then u would do 500 times 240
Mr. Burns measured the heights of 16 apple trees in his orchard. The results are shown in the
dot plot. Which statement about the data is true?
Answer: The 3rd answer on your screen in correct :) imagine cheating
Step-by-step explanation:
Mr. Diaz has 92 peach trees in his orchard which he planted along with apple trees.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
here, we have,
Given, Mr. Diaz has 346 apple trees in his orchard.
Let, 'P' denotes the number of peach trees and 'A' denotes the number of apple trees.
So, A + P = 347.
Also given that he has 162 more apple trees than peach trees in his orchard which is, A = P + 162.
Therefore,
P + 162 + P = 346.
2P = 346 - 162.
2P = 184.
P = 92.
So, Mr. Diaz has 92 peach trees in his orchard.
Q. Mr. Diaz has 346 apple trees in his orchard. He has 162 more apple trees than peach trees in his orchard. How many peach trees does Mr. Diaz have in his orchard?
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