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Leni [432]
3 years ago
9

A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250

pounds and it has uniform density. a = 15 and b = 39.

Mathematics
2 answers:
liq [111]3 years ago
8 0
B hope this helps thanks
Norma-Jean [14]3 years ago
7 0

Answer:

(a) The density of flag is \dfrac{25}{27} Pounds per square foot

(b) The weight of strip is \dfrac{20}{9}(15-h)\Delta h Pounds

(c) The work is \dfrac{20}{9}(15-h)h\Delta h foot-pounds

(d) The exact work by roof is 1250 foot-pounds

Step-by-step explanation:

(a) We are given a flag in the shape of a right triangle.

The total weight of flag is 250 pounds and Uniform density.

Base of the flag =\sqrt{b^2-a^2}

                          =\sqrt{39^2-15^2}=36

Area of the flag =\dfrac{1}{2}\times 36\times 15 = 270

Weight of flag = 250 pounds

Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}

Hence, The density of flag is \dfrac{25}{27}

(b) Weight of strip which is h feet below the roof.

Length of strip =\dfrac{36}{15}(15-h)

Width of strip \Delta h

Weight = Density x area

            =\dfrac{25}{27}\times \dfrac{36}{15}(15-h)

            =\dfrac{20}{9}(15-h)\Delta h

Hence, The weight of strip is \dfrac{20}{9}(15-h)\Delta h

(c) Work slice to move h feet above to the roof

work=Weight\times displacement

       =\dfrac{20}{9}(15-h)\Delta h\times h

       =\dfrac{20}{9}(15-h)h\Delta h

Hence, The work is \dfrac{20}{9}(15-h)h\Delta h foot-pounds

(d) Exact work on the roof by hanging flag

W=\int_0^{15}\dfrac{20}{9}(15-h)hd h

W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}

W=1250-0

W=1250

Hence, The exact work by roof is 1250 foot-pounds

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