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3 years ago

6

How to find the intersection of a circle and parabola?

1 answer:

maria [59]3 years ago

8 0

Use the substitution method to solve for the system of equations:

Circle: (x-h)² + (y-k)² = r²
Parabola: y = a(x-h)² + k or x = a(y-k)² + h

(I am using the "y=" parabola for this example)

Substitute a(x-h)² + k for y into the circle equation and solve for x:
(x-h)² + [(a(x-h)² + k)² - k]² = r²

Then, substitute that x value into the parabola equation to solve for y.

Hope this makes sense!

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sunlight can penetrate a certain Lake to the depth of fifteen meters the lake is five and a half times deeper than the depth of

gizmo_the_mogwai [7]

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3 years ago

A small tree is 80 cm tall.

ruslelena [56]

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7 0

3 years ago

What percent of 30 is 18

Marina CMI [18]

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2 years ago

Read 2 more answers

What’s the answer to number 18 please?!

kozerog [31]

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4 0

3 years ago

The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate

Aloiza [94]

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}$

Volume of cone =

$V = \dfrac{1}{3}\pi r^2 h$

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})$

Putting values, we get,

$\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}$

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

5 0

3 years ago