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Alina [70]
3 years ago
13

Write the standard form of the equation of the circle with the given characteristics.

Mathematics
1 answer:
kati45 [8]3 years ago
4 0
(x – h)^2 + (y – k)^2 = r^2
<span>Where,
(h, k) is the center and </span><span>"r" is the radius.
Substituting the given values:

(x-4)^2 + (y+4)^2 = r^2
</span>
Now using the distance formula. 

<span>r = [(x2-x1)^2 + (y2-y1)^2]^1/2 
</span>
r = [(1 - 4)^2 + (0 + 4)^2]^1/2  
r = [(9+16)]^1/2
r = 25^1/2
r = 5

Substituting the values of r and the center into the main equation:

<span>(x-4)^2 + (y+4)^2 = 25</span>
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Let A(t) be the area of a circle with radius r(t), at time t in min. Suppose the radius is changing at the rate of drdt=6 ft/min
mylen [45]

Answer:

The rate of change is 108\pi ft^(2)/min

Step-by-step explanation:

The area of a circle is given by the following equation:

A(t) = \pi r^{2}

To solve this question, we have to realize the implicit differentiation in function of t. We have two variables, A and r. So

\frac{dA(t)}{dt} = 2\pi r \frac{dr}{dt}

We have that:

\frac{dr}{dt} = 6, r = 9.

We want to find \frac{dA}{dt}

So

\frac{dA(t)}{dt} = 2\pi*9*6

\frac{dA}{dt} = 108\pi

Since the area is in square feet, the rate of change is in ft^(2)/min.

So the rate of change is 108\pi ft^(2)/min

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Step-by-step explanation:

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Point (-1,3) lies in which quadrant ?​
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