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Gennadij [26K]
2 years ago
14

Given that cos θ = –12∕13 and θ is in quadrant III, find csc θ.

Mathematics
2 answers:
Zanzabum2 years ago
8 0

Answer:

A

Step-by-step explanation:

I took the quiz!

Trava [24]2 years ago
7 0

Answer:

A

Step-by-step explanation:

We are given:

\displaystyle \cos(\theta)=-\frac{12}{13},\,\theta\in\text{QIII}

Since cosine is the ratio of the adjacent side over the hypotenuse, this means that the opposite side is (we can ignore negatives for now):

o=\sqrt{13^2-12^2}=\sqrt{25}=5

So, the opposite side is 5, the adjacent side is 12, and the hypotenuse is 13.

And since θ is in QIII, sine/cosecant is negative, cosine/secant is negative, and tangent/cotangent is positive.

Cosecant is given by the hypotenuse over the opposite side. Thus:

\displaystyle \csc(\theta)=\frac{13}{5}

Since θ is in QIII, cosecant must be negative:

\displaystyle \csc(\theta)=-\frac{13}{5}

Our answer is A.

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Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

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(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm y=a^x (where a is a constant) is \dfrac{dy}{dx}=a^x\ln a. Let's use in this in finding the derivative of A(t).

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In the year 2014, t=14.

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6 0
3 years ago
If Jeff washes his car in 6 minutes and bob washes the same car in 8 minutes. How long does it take both of them to wash the sam
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Answer:

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Step-by-step explanation:

Let total job = X

Jeff's rate = X/6

Bob's rate = X/8

Combined rate = X/6 + X/8

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7X/24 = X/T

T = X ÷ (7X/24)

T = X × (24/7X)

T = 24/7 mins

Shortcut:

T = product of individual times/sum of individual times

T = (6×8)/(6+8)

T = 48/14

T = 24/7

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