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3 years ago

I will give brainliest 7k+8=2k-37 Show work pleaseeeee

Mathematics

2 answers:

Artyom0805 [142]3 years ago

6 0

Answer:

k = -9

Step-by-step explanation:

subtract 2k from both sides

_5k+8= -37

subtract 8

_5k = -45

divide by 5

_k = -9

VikaD [51]3 years ago

6 0

Subtract 2k on both sides, to get 5 k +8= -37. Then subtract 8 on both sides to get 5k= -45 Then divide by 5 on both sides to get k= -9.

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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

Read 2 more answers

Using the figure, find x and y

kakasveta [241]

Answer:

x = 8
y = 2√3

Step-by-step explanation:

The triangle is recognizable as a 30°-60°-90° right triangle, which has side length ratios ...

1 : √3 : 2

Side x is thus twice the length of short side 4, so x = 8.

Side y is √3 times the length of short side x-6 = 2, so y = 2√3.

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If you don't happen to recognize the triangle dimensions, you can find x and y using the Pythagorean theorem.

x = √(4² +(4√3)²) = √64 = 8

y = √(4² -2²) = √12 = 2√3

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Express the numbers as a product of its prime factors . Give ur answer in power form

Hitman42 [59]

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3 years ago

One number is 9 times another. Their product is 27 times their sum. Find the numbers.

Lyrx [107]

Answer:

270 & 30

Step-by-step explanation:

let the number is n,

the equation :

n× 1/9 n= 27(n +1/9 n)

1/9 n² = 27n + 3n

1/9 n² = 30n

1/9n²- 30n = 0

n(1/9n -30)= 0

n = 0 or

1/9n = 30 => n = 30×9 = 270

270 is a number,

the other : 270/9 = 30

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3 years ago

Which symbol can be used to correctly compare the two fractions?

aev [14]

Answer:

Step-by-step explanation:

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