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3 years ago

What is the length of the hypotenuse with the given vertex (-5,0)? I

Mathematics

1 answer:

Margaret [11]3 years ago

4 0

Answer:

5000 square ft

Step-by-step explanation:

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Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

1 year ago

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What city was the first capital of the United States?

Wewaii [24]

I believe New York City was the first capital of the US.

3 0

2 years ago

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Which represents the solution set of 5(x+5) <85

Evgesh-ka [11]

You havent added the options

6 0

3 years ago

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John is putting a fence around his garden that is shaped like a half circle and a rectangle. A rectangle has a length of 14 feet

charle [14.2K]

Answer:

Area of the garden = 98 + 19.25 = 117.25 ft²

Step-by-step explanation:

Area of the garden = area of the rectangle + area of the semi-circle

Area of the rectangle = L x B = 14 x 7 = 98 ft²

Area of the semi-circle = 1/2 x πR² = 1/2 x 22/7 x 3.5² = 19.25 ft²

Hence area of the garden = 98 + 19.25 = 117.25 ft²

6 0

3 years ago

The graph of y=|x|y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 999 units.

frosja888 [35]

Answer:

$y = |x| -9$

Step-by-step explanation:

The base function is given as

$y = |x|$

This graph opens up and has its vertex at the origin.

When we shift the graph of this function down by 9 units, its vertex is now at (0,-9)

The equation of this new graph is

$y = |x| -9$

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3 years ago

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