RT is tangent to circle S at point T. If UR = 14, and ST = 8, find RT.

What are the coordinates of Point X? A. (3, –4) B. (–3, –4) C. (4, –3) D. (4, 3)

Greeley [361]

Answer:

3, -4

Step-by-step explanation:

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8 0

3 years ago

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(x +8)(x + 11) = 0 Pls help I’m dumb and don’t know this ...

Ivanshal [37]

Answer:

Step-by-step explanation:

x= -8,-11

5 0

3 years ago

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478 divided 16 using partial quotients

Elena-2011 [213]

29.875 this is ur answer

5 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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In t hours the train has traveled s miles. Find the formula for v, the speed of the train (in mph) in terms of t and s. Find the

Digiron [165]

Answer:

Part 1 .

As per the given statement: In t hours the train has traveled s miles.

Distance of the train = s mile

Time = t hours

Formula for :

Speed of the train(v) = $\frac{\text{Distance of the train}}{\text{Time}}$

or

$v = \frac{s}{t}$ mph .....[1]

Substitute the value of t = 3 hours and s = 180 miles in [1], to solve for v;

$v = \frac{180}{3} = 60 mph$

Therefore, the speed of the train(v) is, 60 mph

Part 2.

Similarly,

The formula for speed of the train (v) is given by;

$v =\frac{s}{t}$

Substitute the value of t = 2.5 hours and s = 225 miles to solve for v;

$v = \frac{225}{2.5} = 90 mph$

Therefore, the speed of the train(v) is, 90 mph

7 0

3 years ago

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