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alexira [117]
3 years ago
14

Write an equation of a line perpendicular to y=4x-3 that contains the point (0,7)

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
8 0

Let k:y=m_1x+b_1 and l:y=m_2x+b_2

l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}

We have

y=4x-3\to m_1=4

Therefore

m_2=-\dfrac{1}{4}

We have the equation of a line:

y=-\dfrac{1}{4}x+b

Put the coordinates of the point (0, 7) to the equation of a line:

7=-\dfrac{1}{4}(0)+b\\\\\7=b\to b=7

Answer: \boxed{y=-\dfrac{1}{4}x+7}

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5.85 m

Step-by-step explanation:

The width of the sand road can be calculated knowing its area and the dimensions of the rectangular garden as follows:

A_{g} = a.b

<u>Where:</u>

Ag: is the area of the rectangular garden

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b: is the width of the rectangular garden = 34 m

A_{s} = 540 m^{2}

<u>Where</u>:

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The relation between the area of the sand road and the area of the rectangular garden is the following:

A_{s} + A_{g} = (a+2x)*(b+2x)

540 m^{2} + 0.5m*34m = ab + 2ax + 2bx + 4x^{2}

557 m^{2} = ab + 2x(a + b) + 4x^{2}

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By solving the above equation for x we have two solutions:

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x₂ = 5.85 m

Taking the positive value, we have that the width of the sand road is 5.85 m.

I hope it helps you!

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