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3 years ago

Find tan2θ if θ terminates in Quadrant IV and cosθ =3/5 .

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

The answer to your question is $\frac{-8}{3}$

Step-by-step explanation:

Data

cos Ф = 3/5

tan2Ф = ?

Quadrant IV

Process

1.- Remember that tanФ = $\frac{Opposite side}{Adjacent side}$ and cos Ф = $\frac{adjacent side}{hypotenuse}$

then, adjacent side = 3 and hypotenuse = 5

2.- Calculate opposite side

O² = h² - a²

O² = 5² - 3²

O² = 25 - 9

O² = 16

O = 4

3.- Calculate the tan 2Ф

tan 2Ф = 2( $\frac{-4}{3}$ ) The opposite side is negative in the fourth

quadrangle

tan 2Ф = $\frac{-8}{3}$

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Multiply c by 9, then add 2 to the result

Novosadov [1.4K]

Answer:

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Step-by-step explanation:

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2 years ago

Of the town's 42 firefighters, 16 volunteered for the special rescue team. Express the portion who did not volunteer.

Doss [256]

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3 years ago

A sociologist wants to know the opinions of employed adult women about government funding for day care. The women were asked to

Zarrin [17]

Answer:

The correct option is C 20.1%.

Step-by-step explanation:

The probability distribution chart representing the opinions of employed adult women about government funding for day care is as follows:

Rating (<em>X</em>) Probability (<em>p</em>)

1 0.110

2 0.206

3 0.464

4 0.201

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2: helpful but not enough

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Thus, the percentage of women who think that the support is sufficient is 20.1%.

The correct option is C.

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2 years ago

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1 year ago

I don’t know how to do this

stich3 [128]

To check for continuity at the edges of each piece, you need to consider the limit as $x$ approaches the edges. For example,

$g(x)=\begin{cases}2x+5&\text{for }x\le-3\\x^2-10&\text{for }x>-3\end{cases}$

has two pieces, $2x+5$ and $x^2-10$ , both of which are continuous by themselves on the provided intervals. In order for $g$ to be continuous everywhere, we need to have

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By definition of $g$ , we have $g(-3)=2(-3)+5=-1$ , and the limits are

$\displaystyle\lim_{x\to-3^-}g(x)=\lim_{x\to-3}(2x+5)=-1$

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The limits match, so $g$ is continuous.

For the others: Each of the individual pieces of $f,h$ are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.

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2 years ago