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3 years ago

There are 20 cars in a lot and three of them leave how many are left

Mathematics

1 answer:

Archy [21]3 years ago

4 0

Answer:

Step-by-step explanation:

becuase 20 -3 = 17

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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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A triangle has angle measurements of 56°, 56°, and 68°. Is this triangle scalene?

slamgirl [31]

Answer:

No. It is an isoceles triangle. A scalene triangle would have NO equal angles.

Step-by-step explanation:

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3 years ago

A tree in Kevin's backyard is 5/8 meters tall. It has been growing for 1 2/5 years. What is the unit rate in meters per year? No

irga5000 [103]

Answer:

o.4464287142 or 0.4

Step-by-step explanation:

The tree is 5/8 meters tall and that's in 1 2/5 years so you would divide them and you get .4464287142

6 0

2 years ago

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Is the equation y = 5x2 linear or not

Effectus [21]

Answer:

yes

Step-by-step explanation:

pretty sure it would be ones u solve the rest.

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2 years ago

Find the factors of 200m2 - 800n2.

leonid [27]

Answer:

Step-by-step explanation:

200m^2-800n^2=200(m^2-4n^2)

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2 years ago