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3 years ago

What is an equation of the line that passes through the points (-6,-3) and (-3,-5)

Mathematics

1 answer:

Murrr4er [49]3 years ago

3 0

Answer:

y = - $\frac{2}{3}$ x - 7

Step-by-step explanation:

A( $x_{1}$ , $y_{1}$ ) , B( $x_{2}$ , $y_{2}$ )

y - $y_{1}$ = m( x - $x_{1}$ )

m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

~~~~~~~~~~~~~

( - 6, - 3 )

( - 3, - 5 )

m = $\frac{-5+3}{-3+6}$ = - $\frac{2}{3}$

y + 5 = - $\frac{2}{3}$ ( x + 3)

y + 5 = - $\frac{2}{3}$ x - 2

y = -  $\frac{2}{3}$  x - 7

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Please help! Find the indicated real n-th roots of x, if any. Give your answer in simplest form.

pishuonlain [190]

1. $\sqrt[6]{64}$

    $2$

2. $\sqrt[3]{128}$

    $1.014096553300555$

3. $\sqrt[10]{1024}$

    $1.01181879913814$

6 0

3 years ago

Find the range of the given function y = 5x - 4, where x > 6.

statuscvo [17]

Given:

The function is:

$y=5x-4$

where $x>6$ .

To find:

The range of the given function.

Solution:

Range is the set of output values.

We have, $x>6$ . It means the value of x is greater than 6 but not equal to 6.

The function is

$y=5x-4$

Putting x=7, we get

$y=5(7)-4$

$y=35-4$

$y=31$

Putting x=8, we get

$y=5(8)-4$

$y=40-4$

$y=36$

Putting x=9, we get

$y=5(9)-4$

$y=45-4$

$y=41$

So, the range of the given function is {31, 36, 41...}.

Therefore, the correct option is B.

7 0

3 years ago

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$