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Masja [62]
2 years ago
8

The point (5,-12) lies on the terminal side of an angel theta in standard position. Find the exact value of cot theta. Express t

he answer as a fraction reduced to the lowest term
Mathematics
1 answer:
saw5 [17]2 years ago
8 0

Answer:

cot\theta=-\frac{5}{12}

Step-by-step explanation:

We are given that the point (5,-12) lies on the terminal side of an angle theta in standard position.

We have to find the exact value of cot\theta.

Let

Point (x,y)=(5,-12)

r=\sqrt{x^2+y^2}

Substitute the values

r=\sqrt{5^2+(-12)^2}

r=\sqrt{169}=13

We know that

cot\theta=\frac{x}{y}

Using values

cot\theta=-\frac{5}{12}

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3 years ago
A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int
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c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

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Since there is no accumulation within the tank, expression is simplified to this:

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The instantaneous amount of salt in the tank is:

m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds

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