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Required shingle bundles = = 668.5 ≈ 669 bundles.

which costs 669 × 35.99 = 24077.31 dollars.

Step-by-step explanation:

Let us divide the roof into two parts 1) cuboid and 2) pyramid.

Now, lower part of the roof

1)  lateral surface of cuboid.

 each surface is a rectangle with length(l) 10.00 m and width(b) 2.32 m

 ⇒ area = l × b = 10 × 2.32 = 23.2 m²

 now, total area of lower part of roof = 4 × 23.2 = 92.8 m²

(4 rectangles / faces)

Now, upper part of the roof.

2) lateral surface of pyramid.

 given length of square base of pyramid (l) = 10.00 m

⇒ diagonal length (d) = 10√2 m.

 now, given total height of roof = 4.36 m

⇒ height of only upper part (pyramid), h = 4.36 - 2.32 = 2.04 m.

Now, one of the pyramid edges (a) , height of the pyramid (h) and half of the diagonal of the square base (d/2) makes a right angled triangle.

From pythagorus theorem,

(height of pyramid)² + (half-diagonal)² = (length of pyramid edge)²

⇒ h² + (d/2)² = a²

⇒ a² = (2.04)² + (50√2)² = 5004.1616

⇒ a = 70.7400 m.

Length of all the edges of pyramid are same in this case,

length of edge, a = 70.7400 m.

Now, consider one triangular face of pyramid with two of the sides being

a = 70.7400 m and 10.00 m

⇒ area of one face of pyramid =

where, p =

(area of triangle with sides a,b,c is )

Here p = .

p = 75.7400 m.

area of one face =

                             = 352.815 m²

Total area of upper part of roof = 4 × 352.815 = 1411.261 m²

Now, total area of roof = 92.8 m² + 1411.261 m² = 1504.061 m².

Given that one bundle of shingles cover 2.25 m²

Required shingle bundles = = 668.5 ≈ 669 bundles.

which costs 669 × 35.99 = 24077.31 dollars.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c