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Rashid [163]
2 years ago
13

Which Table Shows a Proportional Relationship? (no links :)

Mathematics
1 answer:
Vadim26 [7]2 years ago
4 0

Answer:

a

Step-by-step explanation:

as x goes up by 1 y goes up by 4

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1/2 = 1/2
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The sum of three consecutive integers is -15.
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What is the unit rate for meters per second if a car travels 238 meters in 17 seconds?
madreJ [45]
I assume a unit rate is simply ms^-1 or whatever.

In order to determine m/s one must make the "per whatever" part equal to 1. In this case it is seconds, so we must make seconds equal to 1.

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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
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