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3 years ago

PLEEEEASSSSE HELP MEE

Mathematics

1 answer:

IrinaK [193]3 years ago

7 0

Answer:

x = 22.2

Step-by-step explanation:

Let's set up this problem using cosine law:

x^2 = a^2 + b^2 -2abcos110

where a = 12, b = 15

x^2 = (12)^2 + (15)^2 - 2(12)(15)cos110

= 144 + 225 - 360(-0.342)

= 492

x = 22.2

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A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

$x^2+y^2=15^2\to y=\sqrt{225-x^2}$

Then we set the integral for the volume by using shell method:

$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

$u=225-x^2\to du=-2xdx$

The limits of integration also change:

For x=5: $u=225-5^2=200$

For x=15: $u=225-15^2=0$

So the integral becomes:

$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

$=\displaystyle\frac{8000\pi\sqrt{2}}{3}$

5 0

4 years ago

Which functions have an additive rate of change of 3? Select TWO options

Pachacha [2.7K]

Answer:

Second table.

Step-by-step explanation:

A function has an additive rate of change if there is a constant difference between any two consecutive input and output values.

The additive rate of change is determined using the slope formula,

$m = \frac{y_2-y_1}{x_2-x_1}$

From the first table we can observe a constant difference of -6 among the y-values and a constant difference of 2 among the x-values.

$m = \frac{ - 9- - 3}{4-2} = - 3$

For the second table there is a constant difference of 3 among the y-values and a constant difference of 1 among the x-values.

The additive rate of change of this table is

$m = \frac{ - 1 - - 4}{3 - 1} = 3$

Therefore the second table has an additive rate of change of 3.

5 0

3 years ago

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PLEASE HELP I DONT KNOw all THE DEFINITIONS TO THESE- MARK BRAINLIEST TOO

frozen [14]

Answer:

Factor

−

out of

−

(

−

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Step-by-step explanation:

4 0

3 years ago

Jeffrey’s brother Max is 5 years older than twice Jeffrey’s age. Write an expression that represents the relationship of Max’s a

Ede4ka [16]

Answer:

(jx2)+5

Step-by-step explanation:

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3 years ago

Adwadasdawda pls help

yuradex [85]

Answer:

An equation is 92 + 2x = 180.

The congruent angles each measure 44°.

Step-by-step explanation:

1. If two angles in a triangle are congruent and unknown, we can represent that as 2x. That means 92 + 2x = 180.

2. To find the measure of each congruent angle, x, we have to solve the equation above.

Step 1: Simplify both sides of the equation.

$2x + 92 = 180$

Step 2: Subtract 92 from both sides.

$2x + 92 - 92 = 180 - 92$
$2x = 88$

Step 3: Divide both sides by 2.

$\frac{2x}{2} = \frac{88}{2}$
$x = 44$

x = 44 means that the congruent angles each measure 44°.

6 0

3 years ago

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