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Bas_tet [7]
3 years ago
15

Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFraction right-parenthes

is.) and has a slope of StartFraction 3 Over 4 EndFraction.?
y – y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis. = y minus StartFraction 3 Over 4 EndFraction equals StartFraction one-third EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

y – y minus StartFraction one-third EndFraction equals 4 left-parenthesis x minus StartFraction 3 Over 4 EndFraction right-parenthesis. = 4(x – )

y – 4 = y minus 4 equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus StartFraction one-third EndFraction right-parenthesis.(x – )

Mathematics
2 answers:
Alina [70]3 years ago
7 0

Answer:

y-\frac{1}{3}=\frac{3}{4}(x-4)

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

y-y1=m(x-x1)

In this problem we have

point\ (4,\frac{1}{3})

m=\frac{3}{4}

substitute the given values

y-\frac{1}{3}=\frac{3}{4}(x-4)

y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

vaieri [72.5K]3 years ago
5 0

Answer:

B

Step-by-step explanation:

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,
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Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

<u>Pyramid A</u>

s = 4 -- base sides

V = 36 -- Volume

<u>Pyramid B</u>

s = 6 --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

V = \frac{1}{3} * B * h

Where B represents the area of the base equilateral triangle, and it is calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

B = \frac{1}{2} * s^2 * sin(60)

B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}

B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}

B = 4\sqrt 3

The height is calculated from:

V = \frac{1}{3} * B * h

This gives:

36 = \frac{1}{3} * 4\sqrt 3 * h

Make h the subject

h = \frac{3 * 36}{4\sqrt 3}

h = \frac{3 * 9}{\sqrt 3}

h = \frac{27}{\sqrt 3}

To calculate the volume of pyramid B, we make use of:

V = \frac{1}{3} * B * h

Since the heights of both pyramids are the same, we can make use of:

h = \frac{27}{\sqrt 3}

The base area B, is then calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where

s = 6

So:

B = \frac{1}{2} * 6^2 * sin(60)

B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}

B = 9\sqrt 3

So:

V = \frac{1}{3} * B * h

Where

B = 9\sqrt 3 and h = \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}

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