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2 years ago

The center of a circle is at (-5 12) and it has a radius of 16. what is the equation of the circle?

Mathematics

1 answer:

Naya [18.7K]2 years ago

4 0

Answer:

(x+5)^2+(y-12)^2=256

Step-by-step explanation:

Comparing the given (x+5)^2+(y-12)^2=256

to (x - h)^2 + (y - k)^2 = r^2,

we see that h must be -5, k must be 12 and r must be 16. This is the desired equation of the circle with center at (-5, 12) and radius 16.

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Nvm I got it figured out .

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3 years ago

At a copy center, 100 copies cost $4.00. At this rate how much will 450 copies cost?

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2 years ago

Read 2 more answers

A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula

Ilia_Sergeevich [38]

Answer: A. $A'(t)=\frac{4356\pi}{(t+11)^{3}}-\frac{527076\pi}{(t+11)^{5}}$

B. A'(5) = 1.76 cm/s

Step-by-step explanation: Rate of change measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

$A=\pi.r^{2}$

So to find the rate of the area:

$\frac{dA}{dt}=\frac{dA}{dr}.\frac{dr}{dt}$

$\frac{dA}{dr} =2.\pi.r$

Using $r(t)=3-\frac{363}{(t+11)^{2}}$

$\frac{dr}{dt}=\frac{726}{(t+11)^{3}}$

Then

$\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]$

$\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}$

Multipying and simplifying:

$\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$

The rate at which the area is increasing is given by expression $A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$ .

B. At t = 5, rate is:

$A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}$

$A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}$

$A'(5)=\frac{2408693760\pi}{4294967296}$

$A'(5)=1.76268$

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

5 0

2 years ago

What is the equation of the function that is graphed as line a?

valentinak56 [21]

F(x)=-1x-1

1) Pick 2 points on the line (i chose (-4,3) and (3,-4)
2) Find slope of the line using the 2 points. (work below)
3) Find y-intercept, which is the point where y-axis and the line cross (y-intercept is -1).
4) Place both slope and y-intercept into slope-intercept form, y=mx+b (m=slope and b=y-intercept.)
5) Change y to f(x) (meaning function of x).

Work:
3-(-4)/-4-3=3+4/-4-3=7/-7=-1

y-intercept equals -1 also.

y=mx+b
y=-1x+(-1)
y=-1x-1
f(x)=-1x-1<---Answer

6 0

3 years ago

Over a 3.5 year period, 27.5 inches of snow fell in Jackson City. What was the average yearly snowfall in Jackson Cit

Ilya [14]

27.5 / 3.5 = 7.86; The average yearly snowfall was 7.86 inches.

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2 years ago