Write an equation to solve each problem and then solve it. a The sum of three consecutive integers is 84. Find the integers.

Mathematics

1 answer:

otez555 [7]3 years ago

6 0

Answer:

27,28,29

Step-by-step explanation:

Which means that the first number is 27, the second number is 27 + 1 and the third number is 27 + 2. Therefore, three consecutive integers that add up to 84 are 27, 28, and 29. We know our answer is correct because 27 + 28 + 29 equals 84 as displayed above.

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A trough of water is 20 meters in length and its ends are in the shape of an isosceles triangle whose width is 7 meters and heig

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Answer:

a) Depth changing rate of change is $0.24m/min$ , When the water is 6 meters deep

b) The width of the top of the water is changing at a rate of $0.17m/min$ , When the water is 6 meters deep

Step-by-step explanation:

As we can see in the attachment part II, there are similar triangles, so we have the following relation between them $\frac{3.5}{10} =\frac{a}{h}$ , then $a=0.35h$ .

a) As we have that volume is $V=\frac{1}{2} 2ahL=ahL$ , then $V=(0.35h^{2})L$ , so we can derivate it $\frac{dV}{dt}=2(0.35h)L\frac{dh}{dt}$ due to the chain rule, then we clean this expression for $\frac{dh}{dt}=\frac{1}{0.7hL}\frac{dV}{dt}$ and compute with the knowns $\frac{dh}{dt}=\frac{1}{0.7(6m)(20m)}2m^{3}/min=0.24m/min$ , is the depth changing rate of change when the water is 6 meters deep.

b) As the width of the top is $2a=0.7h$ , we can derivate it and obtain $\frac{da}{dt}=0.7\frac{dh}{dt} =0.7*0.24m/min=0.17m/min$ The width of the top of the water is changing, When the water is 6 meters deep at this rate