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Artist 52 [7]
3 years ago
13

The length L of a rectangle is 4 units more than its width W. The rectangle's are is 252 square units. A) Write the equation tha

t you would use to solve this problem by completing the square relating the area to the width. B) What is the width of the rectangle? C) What is the length of the rectangle?
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0

Answer:

w=14

l=18

Step-by-step explanation:

To find the dimensions, create an equation for its area and solve for each using the area formula A = l*w. The dimensions given are A = 252, w for width and l= w+4 (4 more than the width).

A = l*w\\252 = (w+4)*w\\252 = w^2+4w\\252+4 = w^2 +4w +4\\256 = (w+2)^2\\\sqrt{256} =\sqrt{(w+2)^2} \\16 = w+2\\16 = w+2\\14= w\\

The width is 14 so the length is l=w+4 or l= (14)+4 =18

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You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f
postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m   (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m   and   W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L       is  L - 2*x               l =  4 - 2*x

For the side W      is  W - 2*x             w=  2 - 2*x

The height              is  x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x    ⇒  V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x     V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0       8  - 24x + 12x² = 0     reordering    12x² - 24x + 8  = 0

or    3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂  = ( 6 ± √36 - 24 ) /6

x₁,₂  = ( 6 ± 3.46) /6

x₁  =  6 + 3,46 /6     x₁  = 1.58  we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂  =( 6 - 3,46 ) / 6

x₂  = 0,42 m

Dimensions of the open box

l  = 4 - 2*x     l  = 4 - 0,85      l  =  3,15 m

w = 2 -2*x    w  = 2 - 0,85     w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0
2 years ago
Which has the bigger surface area? Jamal's, which is 3 by 3 by 4 ft, or Andy's, which is 4 by 2 by 5 ft and why?
oksano4ka [1.4K]

Jamal-3 x 3 = 9 x 4 = 36


Andy-  4 x 2 = 8 x 5 = 45


Andy's surface area is bigger.

6 0
3 years ago
Solve system of equations for x + y: -4x + 9y = -11 & -3x + 7y =-9
Aloiza [94]

Answer:

x = -3   and   y = -4

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-3x + 7y = -9--------------------------------------------------------------------------(2)

multiply through  equation (1) by 3   and multiply through equation(2) by 4

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subtract equation (1) from equation (2)

y = -3

substitute y = -3 into equation (2)

-3x + 7(-3) = -9

-3x -21 = -9

add 21 to both-side of the equation

-3x -21 + 21 = -9 + 21

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divide both-side of the equation by -3

-3x/-3 = 12/-3

x = -4

x = -3   and   y = -4

8 0
3 years ago
The graphs of functions f(x) and g(x) = f(x) + k are shown below:
Nataly [62]
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7 0
3 years ago
Read 2 more answers
Help pls i don not get it
ss7ja [257]
The answer is 7 hope this helps
3 0
2 years ago
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