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vagabundo [1.1K]
3 years ago
7

A walking path across a park is represented by the equation y=-4x+10. A new path will be built perpendicular to this path. The p

aths will intersect at the point (4,-6). Identify the equation that represents the new path. A. y=4x-22 B. y=1/4x-7 C. y=-4x+10 D. y=-1/4x-5
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
3 0

Given:

The equation of a line is

y=-4x+10

A perpendicular line on the given line passes through the point (4,-6).

To find:

The equation of the perpendicular line.

Solution:

We have,

y=-4x+10

On comparing this equation with slope intercept form y=mx+b, we get

m=-4

So, the slope of the given line is -4.

We know that the product of slopes of two perpendicular lines is always -1.

m\times m_1=-1

(-4)\times m_1=-1

m_1=\dfrac{-1}{-4}

m_1=\dfrac{1}{4}

The slope of the required line is \dfrac{1}{4} and it passes through the point (4,-6). So, the equation of the line is

y-y_1=m_1(x-x_1)

y-(-6)=\dfrac{1}{4}(x-4)

y+6=\dfrac{1}{4}x-1

y=\dfrac{1}{4}x-1-6

y=\dfrac{1}{4}x-7

Therefore, the correct option is B.

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A carpenter is building a rectangular room with a fixed perimeter of 300 ft. what dimensions would yield the maximum​ area?
Inessa05 [86]

Perimeter = 2(Length) + 2(Width)

300 = 2L + 2W → 150 = L + W → 150 - L = W

Area = Length · Width

A_{max} = L(150 - L) → A_{max} = 150L - L²

There are 2 different methods for solving (depending on which math course you are taking).

<u>Calculus</u>: find the derivative, set it equal to zero, and solve for L.

A_{max} = 150L - L² → 0 = 150 - 2L → 2L = 150 → L = 75

<u>Algebra</u>: find the vertex.

A_{max} = - L² + 150L → L = -b/2a → L = -150/2(-1) → L = 75

Once you solve for L, plug it into the Perimeter equation to solve for W:

150 - L = W → 150 - 75 = W → W = 75

Answer: 75ft x 75ft


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