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zmey [24]
3 years ago
7

(c) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 13 square feet.

Mathematics
2 answers:
ra1l [238]3 years ago
5 0

Answer:

Hence, the diagonal of rectangle in terms of width(w) is:

D(w)=\dfrac{\sqrt{169+w^4}}{w}

Step-by-step explanation:

Let the length of the rectangle=l

and width of the rectangle is:w.

We know that the diagonal D of the rectangle is given by with the help of the Pythagorean theorem as:

D=\sqrt{l^2+w^2}-------(1)

Also the area of rectangle(A) is given as:

A=l\times w

Area of rectangle=13=l×w.

l=\dfrac{13}{w}

Hence putting the value of l in equation (1) we get:

D=\sqrt{(\dfrac{13}{w})^2+w^2}=\sqrt{\dfrac{13^2}{w^2}+w^2}\\\\D=\sqrt{\dfrac{169}{w^2}+w^2}=\sqrt{\dfrac{169+w^4}{w^2}}=\dfrac{\sqrt{169+w^4}}{w}

Hence, the diagonal of rectangle in terms of width(w) is:

D(w)=\dfrac{\sqrt{169+w^4}}{w}

Mrrafil [7]3 years ago
3 0
We are asked to express the diagonal of a rectangle in terms of the width in which the area of the polygon is equal to 13 square feet. The area of teh rectangle is equal to length times width. That is 13 = lw; diagonal using pythagorean theorem is sqrt ( l2 + w2). Thus d =  sqrt ( (13/w)2 + w2) = sqrt ( (169/w2 + w2) = sqrt ( (169 + w4)/w2) = 1/w  sqrt (169 + w4)
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Answer:

Please check the explanation.

Step-by-step explanation:

<u>Calculating the area of the outer rectangle:</u>

Given

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  • The width of outer rectangle = w = 5x + 2

Thus,

The area of the outer rectangle:

A = wl

    = (5x + 2) (3x - 1)

    =5x\cdot \:3x+5x\left(-1\right)+2\cdot \:3x+2\left(-1\right)

     =5\cdot \:3xx-5\cdot \:1\cdot \:x+2\cdot \:3x-2\cdot \:1

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<u>Calculating the area of the inner rectangle:</u>

Given

  • The length inner rectangle = l = x + 7
  • The width of inner rectangle = w = x

Thus,

The area of the outer rectangle:

A = wl

   = x(x+7)

   = x² + 7

<u>Calculating the area of the shaded region:</u>

As

The area of the outer rectangle = 15x² + x - 2

The area of the inner rectangle = x² + 7

  • The area of the shaded region can be determined by subtracting the area of the inner rectangle from the area of the outer rectangle.

Thus,

shaded region Area = Outer Rectangle Area - Inner Rectangle Area

                                  = 15x² + x - 2 - (x² + 7)

                                   =  15x² + x - 2 - x² - 7

                                   = 14x² + x - 9

Therefore, the Area of the shaded region is: 14x² + x - 9

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The average score on a standardized test is 750 points with a standard deviation of 50 points. What is the probability that a st
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x=850
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P(x>850)=1-P(x<850)=1-P(z<2)=1-0.9772=0.0228

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