All edges of a cube are expanding at a rate of 2 centimeters per second.
(a) How fast is the volume changing when each edge is 2 centimeter(s)?
(b) How fast is the volume changing when each edge is 14 centimeter(s)?
Answers
Answer:
Part a → dv/dt = 24 cm³/per secondPart b → dv/dt = 1176 cm³/per secondStep-by-step explanation:
As all edges of a cube are expanding at a rate of 2 centimeters per second.
i.e ds/dt = 2 cm/s
The formula of volume of cube: V = s³
Differentiating the volume:
dv/dt = 3s²
Write ds/dt following derivative of volume
dv/dt = 3s² ds/dt
plug in the value: ds/dt = 2 cm/s
dv/dt = (3s²) (2)
dv/dt = 6s²
Given the edge is 2cm.
so plug in the value: s=2
dv/dt = 6s²
= 6(2)²=6(4)=24 cm³/per second
SIMILARLY,
When the edge is 14cm
dv/dt = 6s²
plug in the value: s=14
dv/dt = 6s²
= 6(14)²=6(196)=1176 cm³/per second
Thus,
Part a → dv/dt = 24 cm³/per secondPart b → dv/dt = 1176 cm³/per secondThe volume will be:
(a) 24 cm³
(b) 1176 cm³
Given:
Expanding rate,
2 cm/secLet,
The edge of a cube be "x cm".(a)
When,
x = 2 cmthen,
→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]
Let,
The volume of cube be "V"→ [tex]V = x^3[/tex]
→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]
[tex]= 3\times 2^2\times 2[/tex]
[tex]= 3\times 4\times 2[/tex]
[tex]= 24 \ cm^3[/tex]
(b)
When,
x = 14 cmthen,
→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]
Let,
The volume of cube be "V"→ [tex]V = x^3[/tex]
→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]
[tex]=3\times 14^2\times 2[/tex]
[tex]= 1176 \ cm^3[/tex]
Thus the above answer is correct.
Learn more about cube here:
https://brainly.com/question/11168779
Related Questions
1) Johnny has $15 to spend on songs and podcasts. He wants to download at least 5 items. Songs cost $1.99 each and podcasts cost $0.75 each. Represent the scenario as a system of inequalities.
A. x+y≥5
1.99x+0.75y≤15
B. x+y≤5
1.99x+0.75y≥15
C. x+y≥15
1.99x+0.75y≤5
D. x+y≤15
1.99x+0.75y≥5
2) When solving the following system using elimination, which of the following will allow you to get opposites?
−4x+9y=9
x−3y=−6
A. Multiply the second equation by -3.
B. Multiply the second equation by -4.
C. Multiply the second equation by 3
D. Multiply the second equation by -1.
3) When solving the following system using elimination, which of the following will allow you to get opposites?
−4x−15y=−17
−x+5y=−13
A. Multiply the second equation by -4.
B. Multiply the second equation by 4.
C. Multiply the first equation by -4.
D. Multiply the first equation by -1.
Answers
Answer:
D then B then C
Step-by-step explanation:
sorry if wrong
Bill is going for a run. He runs for 19.2 miles at a speed of 6 miles per hour. For how many hours does he run
Answers
Answer:
3.2miles per hour
Step-by-step explanation:
19.2 / 6 = 3.2
What is the radius of this circle?
A) 2.5 cm
B) 3.14 cm
C) 5 cm
D) 10 cm
WILL MARK BRANLIEST HURRYY
Answers
Answer:
The answer is C 5 cm.
Step-by-step explanation:
Danielle's car wash took in $185 to help raise money for the drama club. Danielle needed to spend $32 for car wash supplies. How much profit did the car wash make?
Answers
Answer:
153 185-32 is 153 so there's your answer
Given that g(x) = −2x+20, find g(−3).
Answers
Answer: 26
Step-by-step explanation:
Okay, so... The new equation would be -2(-3)+20...
So follow the rule of PEMDAS, PEMDAS is;
Parentheses
Exponents
Multiplication
Division
Adding
and Subtracting
Since there are no equations in parentheses and no exponents, we start with multiplication. Which would be -2(-3). ANY parenthesized number beside another number means you must multiply them.
-2(-3) = 6 because a negative multiplied by a negative is a positive..
Now we have 6 + 20 which is 26, so 26 is your answer.
What is the value of z in the equation 4z-15=25
Answers
4(10) - 15 = 25
40 - 15 = 25
Answer:
z=10
Step-by-step explanation:
4z - 15 =25
4z - 15+15 =25+15
4z=40
z=10
If f(x) = x4 – 5, then what is the remainder when f(x) is divided by x + 1?
Answers
Answer:
The remainder is: f(-1) = -4
Step-by-step explanation:
We know that when a polynomial function f(x) is divided by x-c, then the remainder is f(c)
Given the function
[tex]f\left(x\right)\:=\:x^4\:-\:5[/tex]
It is stated that the function f(x) is divided by x + 1.
Thus, substituting x = -1 in the function to find the remainder f(-1)
i.e
f(-1) = (-1)⁴ - 5
f(-1) = 1 - 5
f(-1) = -4
Therefore,
The remainder is: f(-1) = -4
Answer:
9
Step-by-step explanation:
Subtract. Write your answer in simplest form.
3 1/8 - 7/12
A. 2 1/24
B. 3 13/24
C. 2 13/24
D. 3 11/24
Answers
Work:
1) Change the Mixed number into an improper fraction
3 x 8 = 24
1+24 = 25/3
2) Get both fractions on equal terms. Find the Greatest Common Denominator. In this case, it’s 24. Multiply by what you need to get 24. 8x3=24 and 12x2=24
3) Multiply Accordingly
25/8 x 3 = 75/24
7/12 x 2 = 14/24
4) Subtract and change back to Mixed Number
75-14 = 61
61/24 = 2 13/24
Answer:
I believe it is D
Step-by-step explanation:
Richardo had saved $80 from his summer job to buy video games. He
bought 4 games and the cashier gave him $16.40 in change. If each
game cost the same amount, how much was each game?
Leave off the dollar sign in your answer.
Answers
Answer:
$15.90
Step-by-step explanation:
80 - 16.40 = 63.60
63.60÷4 =15.9
15.9 = $15.90
I need help solve this problem
Answers
Answer:
i am not sure of my answer sorry can you make the question simpler maybe then I can answer it
Step-by-step explanation:
13
A local business is calculating the total profit made f(x) after selling
x cupcakes. The business would like to predict their profit by creating an equation for the function.
Write an equation that models the total profit for the business below.
Drag and drop the numbers into the boxes to create the function's equation. Not all numbers listed will be used.
x | f(x)
_____
3 | -5
7 | -2
11 | 1
15 |4
(it won’t allow me to send another pic with the chart so i hope this helps. & the picture i did attach are the things you have to use to create the problem it has to be in the form f(x) = _ x + _
Answers
Answer:
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
Step-by-step explanation:
We need to find equation from the table given
x f(x)
3 -5
7 -2
11 1
15 4
We can write equation in the form of [tex]y=mx+b[/tex]
where m is slope and b is y-intercept.
Finding Slope
We can used the slope formula to find slope: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table we have: [tex]x_1=3, y_1=-5, x_2=7, y_2=-2[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}[/tex]
So, we get slope [tex]m=\frac{3}{4}[/tex]
Now, finding y-intercept
Using the slope [tex]m=\frac{3}{4}[/tex] and point (3,-5) we can find y-intercept
[tex]y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}[/tex]
The y-intercept is [tex]b=\frac{-29}{4}[/tex]
So, the equation having slope [tex]m=\frac{3}{4}[/tex] and y-intercept [tex]b=\frac{-29}{4}[/tex] will be:
[tex]y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}[/tex]
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
Sam and his family go out to eat for his birthday. The total bill is $123.79. The tax on his meal is 8.25%. What is the total amount he will pay for the bill not including the tip for the waitress
please help
Answers
Answer:
It will come out to about $134 even.
Mark brainlyest if this helps
Step-by-step explanation:
What sum is represented by the arrow diagram?
Answers
Answer:
Would it be 1?
Step-by-step explanation:
I'm not that sure but it seems it goes up to 4 so 4- -3 = 1. Exuse me if my wrong..
PLSSS HELP WILL GIVE BRAINLIEST FOR FIRST CORRECT ANSWER!!!!!!!!!
If a fair die is rolled once, what is the probability of one
An odd number
A number greater than 2
A square number?
Answers
Answer:
A fair die has 6 sides.
There are 3 odd numbers on a fair die so the probability would be 3/6
There are 4 numbers greater than 2 on a fair die o the probability of that would be 4/6
There is only one number that will make it square and that is 4. So the probability would be 1/6
Jack and Jill are walking toward each other on a path. When they start out they are 15 miles apart. Jack walks at a pace of 1.5 miles per hour. Jill walks at a pace of 2 miles per hour. How far apart will they be after 4 hours.
Answers
Answer:
1 mile
Step-by-step explanation:
Step one:
given
total distance = 15miles
Jack walks at a pace of 1.5 miles per hour
after 4 hours he will cover a distance of
1.5*4= 6 miles
Jill walks at a pace of 2 miles per hour
after 4 hours he will cover a distance of
2*4= 8 miles
Step two:
The total distance jack and jill must have covered after 4 hours is
8+6= 14 miles
the distance apart will be 15-14= 1 mile
-42=-7+5x
Solve for x
Answers
Answer:
x = -7
Step-by-step explanation:
-42=-7+5x
-42 + 7 = 5x
5x = - 35
x = -35/5
x = - 7
Hope it helps!
Answer:
x = -7
Step-by-step explanation:
Given equation:
[tex]-42 = -7 + 5x[/tex]
Simplify the equation.[tex]-42 = 5x -7[/tex]
2. Flip the equation.
[tex]5x + 7 = -42[/tex]
3. Add 7 to each side.
[tex]5x - 7 + 7 = -42 + 7[/tex]
[tex]5x = -35[/tex]
4. Divide both sides by 5.
[tex]\frac{5x}{5}[/tex] = [tex]\frac{-35}{5}[/tex]
5. Divide the fraction.
[tex]-35[/tex] ÷ [tex]5[/tex] = [tex]-7[/tex]
please help idk the answers i miissed the entire lesson
Answers
Answer:that might be a post it i’ve slope. but i’m not sure.
here’s something to help!
Step-by-step explanation:
i need help with surface area
Answers
Cube SA=6s^2 s =length of the side
Prism SA= 2B + ph B = area of the base. P = perimeter of the base. H =height
HELPPP PLSSS lol help
Answers
Answer:
1)48
2)25
3)21
Step-by-step explanation:
Answer:
8:48
5:25
21:35
Step-by-step explanation:
for any ratio, it stays the same if you multiply left and right with the same number.
So let's take the last one:
3 : 5 should be equivalent to ? : 35
How did 5 get to be 35? It was multiplied by 7.
So we do that on the left side as well.
3×7 = 21.
Conclusion: 21:35 is equivalent to 3:5
What is 10and 1 half divided by 7 eights
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
10 1/2 / 7/8= 12
Given the quadratic equation: f(x) = x2+4x-21
What are the factors of the quadratic (factored form/intercept form)? Show your work.
PLEASE HURRY
Answers
[tex]f(x)=x^2+4x-21\\f(x)=(x+7)(x-3)[/tex]
These are x-intercepts form. So the answer is (x+7)(x-3).
I WILL GIVE YOU THE BRAINIEST!!!
In a company, 60% of the workers are Men. If 2,320 people work for the company who aren't men, how many workers are there in all?
If Right.
Answers
Answer: 1392 people who work for the company are men.
I did this by multiplying 2320 by 0.6, which got me my answer.
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
PLEASE help. I will mark as brainliest
Answers
Answer:
C 35
Step-by-step explanation:
Brainliest
PLEASE HELP!!!
Problem #1
A groundskeeper needs grass seed to cover a circular field, 580 feet in diameter.
A store sells 100-pound bags of grass seed. One pound of grass seed covers about 800 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field? Explain or show your reasoning.
Step1: Find the area of the circular field.
Step2: Find how many square feet covers a 100-pound bag(1pound covers 800 sq. ft)
Step 3: Find how many bags are needed to cover the entire area found on step1?
Step 4: Make sure to tell the number of bags that you need to cover the entire area of the field.
Answers
(Is this question not too complex)
Ask the questions one-by-one.
Isaiah spent $19.60 on a gift for his mother. The amount that he spent on the gift was StartFraction 5 over 7 EndFraction of the total amount that he spent at the store.
Which statements can be used to find x, the total amount that Isaiah spent at the store? Select three options.
A. StartFraction 5 over 7 EndFraction = StartFraction x over 19.60 EndFraction
B. StartFraction 5 over 7 EndFraction x = 19.60
C. StartFraction 5 over 7 EndFraction (StartFraction 7 over 5 EndFraction) x = 19.60 (StartFraction 7 over 5 EndFraction)
D. StartFraction 5 over 7 EndFraction (StartFraction 7 over 5 EndFraction) = StartFraction x over 19.60 EndFraction (StartFraction 7 over 5 EndFraction)
E. x = 27.44
Answers
Answer:
B,C and E
Step-by-step explanation:
I did the test
Answer:
that one dude is correct i can confirm this like frfr
Step-by-step explanation:
Please help. I’m struggling to answer this
Answers
Answer:
[tex]\frac{35}{18}[/tex] π m
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{50}{360}[/tex] ( r is the radius )
= 2π × 7 × [tex]\frac{5}{36}[/tex]
= [tex]\frac{70}{36}[/tex] π
= [tex]\frac{35}{18}[/tex] π
. Which expression is NOT equal to 28? o A 1.288 = 46 B 1 820 = 65 C. 1456 - 52 D 1107 = 42
Answers
Aye plz help. Im abt to die. Find the perimiter of the shape below.
Answers
Answer:
40
Step-by-step explanation:
Add all the sides together which is 40
Answer:35
Step-by-step explanation:
Helppppp
Thank You!!!
Answers
Answer: B and C
Step-by-step explanation: To start off, you subtract 3 from both sides, to get 4<z/2, then multiply both sides by 2, you get z>8. Now it's greater than 8, so it can't equal 8, so the answers would be B and C, since they are both greater than 8, and you have to select multiple choices.
Use the distributive property to write an equivalent expression.
6(y-8z+7)
6(y−8z+7)
Answers
Answer:
6y - 48z + 42
Step-by-step explanation:
6 ( y - 8z + 7 )
= 6y - 48z + 42
so you distribute the 6
so it’d be 6 x y which is 6y
6 x -8z which is -48z
6 x 7 which is 42
put it together
final answer: 6y-48z+42