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3 years ago

PLZ HELP ANSWER BY TODAY

Mathematics

1 answer:

Ivahew [28]3 years ago

7 0

X = 29

Explanation:

Rigt angle means 90°

Here 2x + 32 = 90

so, 2x = 90 - 32

2x = 58

x = 58÷2

x = 29

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The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute. At the instant when the volume of

Inessa05 [86]

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere, of radius r, is given by:

$V = \frac{4\pi r^3}{3}$

<h3>What is the surface area of a sphere?</h3>

The surface area of a sphere, of radius r, is given by:

$S = 4\pi r^2$

<h3>What is the rate of change?</h3>

Applying <em>implicit differentiation</em>, the rate of change of both the volume and the surface area can be found, as follows:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$\frac{dS}{dt} = 8\pi r\frac{dr}{dt}$

Volume of 3131 cubic centimeters, hence:

$V = \frac{4\pi r^3}{3}$

$\frac{4\pi r^3}{3} = 3131$

$4\pi r^3 = 3(3131)$

$r = \sqrt[3]{\frac{3(3131)}{4\pi}}$

$r = 9.0754$

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:

$\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}$

$-9988 = 4\pi (9.0754)^2\frac{dr}{dt}$

$\frac{dr}{dt} = -\frac{9988}{4\pi (9.0754)^2}$

$\frac{dr}{dt} = -9.651$

Then, the <u>rate of change of the surface area</u> of the sphere is given by:

$\frac{dS}{dt} = 8\pi (9.0754)(-9.651) = -2201.293$

The rate of change of the surface area of the sphere -2201.293 square centimeters per second.

To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353

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3 years ago

Find the midpoint and distance of the line segment AB connecting the two points: A(- 4, 5) and B(0, 8)

Brums [2.3K]

The midpoint is -4,5

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3 years ago

f five times a number is subtracted from twelve times a number, the result is seven less than twice the number. Find the number

gayaneshka [121]

12x-5x=2x-7
7x=2x-7
x=-7/5

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4 years ago

a cylindrical vase has a diameter of 6 inches at the bottom of the vase there are 9 marbles each of diameter 3 inches the vase i

KiRa [710]

Answer:

<h2>The volume of water in the vase is 339.33 in^3</h2>

Step-by-step explanation:

To calculate the volume of water in the vase we need the following parameters

1. the diameter/radius of the vase

2. the height /level of water in the vase

Given data

diameter d= 6 in

radius = d/2= 6/2 = 3 in

height of water h= 12 in

we know that the expression for the volume of a cylinder is given as

$volume= \pi r^2h$

Inserting our data we have

$volume= 3.142*3^2*12\\\volume= 3.142*9*12\\\volume= 339.33 in^3$

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3 years ago

What are the solutions of the equation Z ^ 2 - 6z - 27 equals 0

Leona [35]

Z^2 - 6z - 27 = 0 you need to factor out firts then solve for z
(z+3 )(z-9) = 0
z+ 3 = 0
z = -3

z-9= 0
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