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elena55 [62]
3 years ago
10

Select the correct answer from each drop down menu. In the figure, AB=__inches and AC=___

Mathematics
2 answers:
BaLLatris [955]3 years ago
4 0

Answer: In the figure AB is about 8.4 inches and AC is about 13.05 inches.

Step-by-step explanation: We can use cosine to find the hypotenuse. cos(40)=\frac{10}{x} \\cos(40) (x)=\frac{10}{x}(x)\\cos(40) (x) =10\\\frac{cos(40) (x)}{cos (40)} =\frac{10}{cos (40)} \\x=\frac{10}{cos(40)}

Using a calculator x is about 13.05

Using tangent we can find the length opposite of <C

tan(40)=\frac{x}{10} \\tan(40) (10)=\frac{x}{10}(10)\\tan(40) (10) = x

Using a calculator x would be about 8.4

inysia [295]3 years ago
4 0

Answer:

Step-by-step explanation:

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Quadrilateral ABCD quadrilateral WXYZ. If AD = 12, DC = 6, and ZY = 36, find WZ.
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Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the
sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let y(t) be the depth of water in the barrel at time t,  where y is measured in inches and t in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

                                                 \frac{dy}{dt}=-k\sqrt{y}

where k is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by \frac{1}{\sqrt{y}}

\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k

Multiply by dt

\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt

Take integral

\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt

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We know that the water level starts at 36, this means y(0)=36. We use this information to find the value of C.

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So our formula for the depth of water in the barrel is

y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\

To find the time, t, at which all the water leaks out of the barrel, we solve the equation

\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

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