Mathematics, 08.11.2019 05:31 eldercunningham

Arectangular hole is to be cut in a wall for a vent. if the perimeter of the hole is 112 in. and the length of the diagonal is a minimum, what are the dimensions of the hole? let the length and width of the hole be x and y, respectively, and let the length of the diagonal be d. find an equation that describes the quantity to be minimized. upper d squared equals x squared plus (56 minus x )squared (type an equation.) the length of the diagonal is a minimum when the hole is 28 in. by 28 in.

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Answer from: hailiemanuel930

D = √ (2x² -112x + 3136

Step-by-step explanation:

From problem statement we have:

Perimeter of the hole P = 112 in

length of the hole x

wide of the hole y

Perimeter is by definition P = 2*x + 2*y so y = [( P - 2* x)] ÷ 2

y = ( P - 2*x ) ÷ 2 and P = 112 in

y = ( 112 - 2*x) ÷ 2 ⇒ y = 56 - x (1)

Triangle ABC (see attached file) is straight in A. Then diagonal D is:

D² = x² + y² from equation (1) D² = x² + ( 56 - x )²

Solving: D² = x² + 3136 + x² - 112*x ⇒ D² = 2*x² - 112*x + 3136

Finally D = √ (2x² -112x + 3136

Answer from: heartykwarteng12

1. The slope of the diagonal can be determined by the formula rise/run where "rise" is the change in y and "run" is the change in x. Since we know that the y coordinate of B and A are the same, "rise" would be equal to zero therefore the slope would immediately be zero.

ANSWER: The slope of diagonal AB is 0.

2. The general equation of any line is determined by y = mx + b where m is the slope of the line and b is its y-intercept. Since we know that the slope is equal to zero, we just need to find the y-intercept. It is evident in the graph that the line passes through y = -2 therefore this would be the intercept.

The equation would then be y = -2. We just add some restrictions to its domain since the values of x of line AB only runs from -2 to 2.

ANSWER: Its equation is y = -2

{x | -2 ≤ x ≤ 2}.

Answer from: drzewostan5716

see explanation

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = P(- 2, 2) and (x₂, y₂ ) = Q(2, 2)

m = $\frac{2-2}{2+2}$ = $\frac{0}{4}$ = 0 ← slope of line PQ

This indicates the line PQ is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (- 2, 2) and (2, 2) with y- coordinates of 2

Thus y = 2 ← equation of line PQ

Answer from: dianereyes7475

slope = 0, equation is y = - 2

step-by-step explanation:

the endpoints of ab are a(- 2, - 2) and b(2, - 2)

since the y- coordinates are equal both - 2 then the line is horizontal and parallel to the x- axis with slope = 0

the equation of a horizontal line is y = c

where c is the value of the y- coordinates the line passes through

in this case the line passes through points with y- coordinate of - 2

hence equation of ab is y = - 2

Answer from: michellebreshears451

The answer to your question is slope = 0; y = -2

Step-by-step explanation:

Data

A (-2, -2)

B (2, -2)

Process

1.- Calculate the slope

m = (-2 - (-2)) / (2 - (-2))

m = ( -2 + 2) / (2 + 2)

m = 0/4

m = 0

2.- The equation of the line is

y - y1 = m(x- x1)

y - (-2) = 0(x - (-2))

y + 2 = 0

y = -2

Answer from: venuscagle

A and its equation is b

Answer from: gilcarrillo146

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line that passes through theses points will be:
m=(y₂-y₁)/(x₂-x₁)

We have two points A(-2,-2) and B(2,-2); therefore the slope will be:
m=(-2+2)/(2+2)=0/4=0

slope-intercept form:
y=mx +b
m=slope
b=y-intercept =-2

y=0x-2
y=-2

The slope of diagonal AB is 0 and its equation is y=-2

Answer from: jasminer257

Given two points (x₁,y₁) and (x₂,y₂) the slope of the line that passes through theses points will be:m=(y₂-y₁)/(x₂-x₁)
We have two points A(-2,-2) and B(2,-2); therefore the slope will be:m=(-2+2)/(2+2)=0/4=0
slope-intercept form:y=mx +bm=slopeb=y-intercept =-2
y=0x-2y=-2
The slope of diagonal AB is 0 and its equation is y=-2

Answer from: tianna08

Hello there.

The slope of diagonal PQ is , and its equation is
The slope of diagonal PQ is zero, and its equation is y = 2.

Answer from: Galaxie85111

Slope = Rise/Run

Given:
Rise = 0
Run = 5

Therefore,
Slope = 0/5
= 0
The general form of a linear equation is :
y = mx + b

m = slope
b = y-intercept

Given:
Slope = 0
Y-intercept = -2

Hence,
Equation is : y = -2

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