Mathematics, 09.07.2019 06:30 Zieken993

Aflag 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.

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Answer from: terry94

(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

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

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

Answer from: Quest

If gravity is one third on mars then weight also one third on mars

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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Aflag in the shape of a right triangle is hung over the side of a building as shown below. the total...