What is the radius of a circle that has a circumference of 1

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Vlad [161]

Answer:

192 cubic inches

Step-by-step explanation:

8 0

3 years ago

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Find the Length of ST

vfiekz [6]

Step-by-step explanation:

Consider Similarity and enlargement

To get the enlargement factor,

Take the ratio result of any two similar sides. i.e

PQ/AB = 3.6/2 = 1.8

The enlargement factor is 1.8

To get ST, consider ED then multiply it by the enlargement factor. i.e

= 5 x 1.8

= 9

7 0

3 years ago

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

2 years ago

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Find the value of y. Please help

Alex_Xolod [135]

if the ∡E = ∡F = 90°, that means for that quadrilateral of BEGF, the other angles are ∡B = ∡G = 90°, which means is a square, meaning all its sides are equal, therefore

$\bf y + 5 = 3y\implies 5=2y\implies \cfrac{5}{2}=y\implies 2\frac{1}{2}=y$

4 0

3 years ago

What is the factored form of x^3 + 2x^2 + 2x?

sveta [45]

X
(
x
+
1
−
ı
)
(
x
+
1
+
ı
)
x(x+1−ı)(x+1+ı)

6 0

4 years ago

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