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3 years ago

How many total cups of orange paint will this mixture yield?

Mathematics

1 answer:

DIA [1.3K]3 years ago

7 0

Answer:

At least 6 but are there answer choices or at least a picture of the mixture

~ Zachary

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The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When

atroni [7]

Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

$A=w\ell$

Where w is the width and l is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to t, where w and l are both functions of t:

$\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]$

By the Product Rule:

$\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w$

Since we know that dl/dt = 6 and that dw/dt = 5:

$\displaystyle \frac{dA}{dt}=5\ell + 6w$

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

$\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}$

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

8 0

3 years ago

Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is i

Romashka-Z-Leto [24]

0.08 cm/min

Step-by-step explanation:

Given:

$\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}$

Find $\frac{dr}{dt}$ when diameter D = 20 cm.

We know that the volume of a sphere is given by

$V = \dfrac{4\pi}{3}r^3$

Taking the time derivative of V, we get

$\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}$

Solving for $\frac{dr}{dt}$ , we get

$\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})$

$\:\:\:\:\:\:\:= 0.08\:\text{cm/min}$

3 0

2 years ago

Solve for j: j + j / 2 + J + 5 = 45

Georgia [21]

Answer:

j:5j/2+5=45 Or j=16 how you put it was a little confusing

5 0

2 years ago

Write the equation of the line that passes through the points ( – 3, 2) and ( - 1,6).

bekas [8.4K]

Answer:

the answer is y=2x+8

Step-by-step explanation:

6 0

2 years ago

Will mark brainliest and rate 5/5

Levart [38]

Answer: Usually the formula for the volume of a prism is V=b(h)—> In words, Volume equals base times height. This means the height 10 would replace h. —> V=b(10). Next we want to find the B in the forumla. If you notice the question says that the base is 24 square centimeters. So our new formula is V=24(10). So option C, V=24x10 is the correct answer.

8 0

2 years ago