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Mathematics, 02.01.2021 06:30 rb161040

I need it step by step please

I need it step by step please

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Answers: 3

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Answer from: josebienka

The equation of the line passes through (3, -2) and parallel to the given line:

y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line:

$y=-\frac{1}{3}x-1$

Step-by-step explanation:

Given the points on the graph line

(2, -1)

(1, -4)

Finding the slope between (2, -1) and (1, -4)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:-4\right)$

$m=\frac{-4-\left(-1\right)}{1-2}$

m=3

Equation of the line passes through (3, -2) and parallel to the given line.

We know that parallel lines have the same slope.

so the equation of the line parallel to the given line = 3

Thus, using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 3 and the point (3, -2)

y - (-2) = 3(x-3)

y+2 = 3x-9

y = 3x-9-2

y = 3x-11

Therefore, the equation of the line passes through (3, -2) and parallel to the given line:

y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = 3

perpendicular slope = – 1/m = -1/3 = -1/3

Therefore, substituting the values of perpendicular slope = -1/3 and the point (3, -2) in the point-slope form of the line equation

$y-\left(-2\right)=-\frac{1}{3}\left(x-3\right)$

$y+2=-\frac{1}{3}\left(x-3\right)$

subtract 2 from both sides

$y+2-2=-\frac{1}{3}\left(x-3\right)-2$

$y=-\frac{1}{3}x-1$

Therefore, the equation of the line passes through (3, -2) and perpendicular to the given line:

$y=-\frac{1}{3}x-1$

Conclusion:

The equation of the line passes through (3, -2) and parallel to the given line:

y = 3x-11

The equation of the line passes through (3, -2) and perpendicular to the given line:

$y=-\frac{1}{3}x-1$

ansver

Answer from: Quest

answer: yes i agree that you should not put it on/p>

step-by-step explanation: the reason for this is that it wastes other peoples time and also make them fail as well and that is never good.

ansver

Answer from: Quest

Hello!

the answer is:

the correct option is the option b.

$surfacearea=126\pi units^{2}$

why?

to calculate the surface area of the right cylinder, we need to use the following formula:

$surfacearea=2\pi rh+\pi r^{2}$

from the picture we know that:

$h=2units\\r=7units$

so, substituting and calculting we have:

$surfacearea=2\pi rh+\pi r^{2}surfacearea=2*\pi *7*2+2*\pi *7^{2}=28\pi + 98\pi =126\pi units^{2}$

hence, we have that the correct option is the option b.

$surfacearea=126\pi units^{2}$

have a nice day!

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