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2 years ago

Complete the equation of the line through (−10,−7) and (-5,-9). Use exact numbers.

Mathematics

1 answer:

Agata [3.3K]2 years ago

5 0

Step-by-step explanation:

(y+7)/(-9+7) = (x+10)/(-5+10)

(y+7)/(-2) = (x+10)/5

5(y+7)=-2(x+10)

5y+35= -2x-20

the equation :

5y=-2x-20-35

devided by 5

=> y = -2/5 x - 11

or y = -0.4x - 11

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Is f(x)=3/4 a function?

Marat540 [252]

Answer:

Yes, f(x) = $\frac{3}{4}$ is a constant function.

Step-by-step explanation:

A function is defined to be a relation from 1 set of numbers to another set of numbers.

The main condition for a relation to be a function is that for every number in the domain there should be a <u>unique image</u>

Here the given function is f(x) = $\frac{3}{4}$

This function is a constant function and gives the value 0.75 for all values of x.

Hence the graph would be a straight line parallel to the x-axis passing through y = 0.75.

Hence the f(x) = 0.75 is a function.

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3 years ago

Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d

algol13

You want to find the volume inside the hemisphere $x^2+y^2+z^2=4$ (i.e. inside the sphere but above the plane $z=0$ ) and outside the cylinder $x^2+y^2=1$ . Call this region $R$ .

In cylindrical coordinates, we have

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$

$\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr$

$\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du$

(where $u=4-r^2$ )

$\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du$

$=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi$

7 0

3 years ago

A pentagon has 3 congruent sides and 2 other congruent sides. The perimeter of the pentagon is 36 centimeters. The three long co

zvonat [6]

The answer is c. ...

6 0

2 years ago

Read 2 more answers

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Allisa [31]

Answer:

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2 years ago

Steve's sister is 25 years old. her age is 5 years more than 4 times his age.

Virty [35]

Answer:

Steve is 5

Step-by-step explanation:

Steves sister is 25, she is 5 years more than 4 times steve is.

5 * 4 = 20 and the sister is 5 years older so,

Steve is 5

6 0

3 years ago