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mamaluj [8]
3 years ago
11

1 quart is equal to 4 cups given this fact what is 8 quarts equivalent to in cups

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
5 0
8 quarts is equal to 32 cups :)
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The circumference of the circle is increasing at a rate of 0.5 meters per minute. What's the rate of change of the area of the c
morpeh [17]

Answer:

The rate of change of the area of the circle when the radius is 4 meters = 2 meters²/minute ⇒ answer 4

Step-by-step explanation:

* Lets revise the chain rule in the derivative

- If dy/da = m and dx/da = n, and you want to find dy/dx

∴ dy/dx = dy/da ÷ dx/da = m ÷ n = m/n

* In our problem we have

- The rate of increasing of the circumference dC/dt = 0.5 meters/minute

- We need the find the rate of change of the area of the circle

 when the radius is 4 meters

- The common element between the circumference and the area

 of the circle is the radius of the circle

* We must to find dC/dr and dA/dr and use the chain rule to

 find dA/dr

- Find the rate of change of the radius dr/dt

∵ C = 2πr

- Find the derivative of C with respect to r

∴ dC/dr = 2π ⇒ (1)

∵ dC/dt = 0.5 meters/minute ⇒ (2)

- Divide (1) by (2) to get dr/dt by using chain rule

∵ dC/dt ÷ dC/dr = 0.5 ÷ 2π

∴ dC/dt × dr/dC = 0.5 × 1/2π ⇒ cancel dC together and change

   0.5 to 1/2

∴ dr/dt = 1/2 × 1/2π = 1/4π ⇒ (3)

- Find the rate of change of the area dA/dt

∵ A = πr²

- Find the derivative of A with respect to r

∴ dA/dr = 2πr

∵ r = 4

∴ dA/dr = 2π(4) = 8π ⇒ (4)

- Multiply (4) by (3) to get dA/dt by using chain rule

∵ dA/dr × dr/dt = 8π × 1/4π ⇒ divide 8 by 4 and cancel π

∴ dA/dt = 2 meters²/minute

* The rate of change of the area of the circle when the radius is

  4 meters = 2 meters²/minute

3 0
3 years ago
Can someone please clearly explain how to correctly work out Q6? Much appreciated
steposvetlana [31]

s =1/2(u+v)t

u = 16, v=16, t=90

s = 1/2(16+16)90

s = 1/2(36)90

s = 16*90

s = 1440

4 0
3 years ago
What percent can you change 8/57 into and how?
Elena L [17]
14.0351% is the answer i’m pretty sure
5 0
3 years ago
Read 2 more answers
Question 2
Afina-wow [57]

Given:

A dilation centered at the origin with a scale factor of 2 can be denoted

with the following notation:

D_2(x,y)=(2x,2y).

To find:

The D_4 for point  A (-2, 3).

Solution:

If D_2(x,y)=(2x,2y), then

D_4(x,y)=(4x,4y)

Substitute x=-2 and y=3 in the above rule to find D_4 for point  A (-2, 3).

D_4(-2,3)=(4(-2),4(3))

D_4(-2,3)=(-8,12)

Therefore, D_4 for point  A (-2, 3) is (-8,12).

3 0
3 years ago
-3w-4+5w=32 what is the solution?
Hunter-Best [27]

Answer:

w = 18

Step-by-step explanation:

Step 0: Set up the equation

=> -3w - 4 + 5w = 32

Step 1: Move the same variable together

=> -3w + 5w = 32 + 4

Step 2: Add up and simplify

=> 2w = 36

Step 3: Divide both by 2

<u>=> w = 18</u>

7 0
2 years ago
Read 2 more answers
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