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2 years ago

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An object falls 3 meters during the first second, another 15 meters during the second second, and then 75 meters more during the

third second. If this pattern continues, how far does the object fall during the first 4 seconds?

1 answer:

Lana71 [14]2 years ago

8 0

3 times 5 equals 15
15 times 5 equals 75
75 times 5 equals 375
hope this helped (:

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Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

<u>Slope of a line</u><u> :-</u>

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

<u>Parallel lines:-</u>

<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel

<u>Perpendicular lines:-</u>

<u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

<u>Step 2</u>:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

<u>Step 3</u>:-

b) <u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

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

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Correct answer is D.

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\\ \text{common in the numerator is }
\\
\\ 10x^3y^2
\\
\\ \text{so}
\\
\\ \frac{10x^3y^2(x^3y + 2)}{5x^3y}
\\
\\ \text{cancel common factors... }
\\
\\ 2y(x^3y + 2) = 2x^3y^2 + 4y$

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