Mathematics College

A new linear road is planned to be constructed perpendicular to an existing one. On a representative grid, a surveyor determines that the existing linear road passes through the points LaTeX: (4,7)( 4 , 7 ) and LaTeX: (2,15)( 2 , 15 ). The roads must intersect at the point LaTeX: (4,7)( 4 , 7 ).

(a) Determine the slope of the new road.

(b) Determine the equation of the new road.

Answers

Answer 1
Determine the equation of the new road
Answer 2

a) The slope of the new road is given by m = -4

b) The equation of line is y = -4x + 32

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P ( 4 , 7 )

Let the second point be represented as Q ( 2 , 15 )

Now , the slope is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 15 - 7 ) / ( 2 - 4 )

Slope m = 8 / -2

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = ( -4 ) ( x - 7 )

On simplifying the equation , we get

y - 4 = -4x + 28

Adding 4 on both sides of the equation , we get

y = -4x + 32

Hence , the equation of line is y = -4x + 32

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Related Questions

The position of a particle on a straight line is given by s(t) = 3 – cos(t).
A. Find velocity and acceleration at t = 4.3 s.
Round your answers to 2 decimal(s).
v(t) =
a(t) =

Answers

Given the position function

s(t) = 3 - cos(t )

differentiate once to get the velocity, and twice to get the acceleration:

v(t) = s'(t) = sin(t )   →   v (4.3 s) ≈ -0.92

a(t) = s''(t) = v'(t) = cos(t )   →   a (4.3 s) ≈ -0.40

The acceleration is negative, so the particle is slowing down.

the diameter of a circle is 7 m. find its area and perimeter.Answer fast!!!!!
​

Answers

Answer:

Area≈38.48m²

perimeter≈43.98

The Area is 38.48 and the Perimeter is 21.99
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