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3 years ago

What the answer now answer only if now answer corry

Mathematics

1 answer:

goblinko [34]3 years ago

6 0

Answer:

Approximately 11.5 units.

Step-by-step explanation:

We need to find the side opposite to ∠W. We are given the two angles ∠W and ∠X. We are also given that Side X is equal to 7. Therefore, we can use the Law of Sines.

Now, like last time, use the Law of Sines:

$\frac{\sin(V)}{v}=\frac{\sin(W)}{w}=\frac{\sin(X)}{x}$

We can ignore the first term. Plug in 144 for ∠W, 21 for ∠X, and 7 for <em>x</em>.

$\frac{\sin(144)}{w}=\frac{\sin(21)}{7}$

Cross multiply:

$7\sin(144)=w\sin(21)\\w=\frac{7\sin(144)}{\sin(21)} \\v\approx11.4812\approx11.5$

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Hong rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 90 cents for each mile dr

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Answer: Hong drove the truck for 294 miles.

Step-by-step explanation:

Let m represent the number of miles for which he drove the truck.

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2 years ago

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

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Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

$\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}$

$\sin(\beta) *\dfrac{1 }{\cos(\beta) }$

$\dfrac{\sin(\beta)}{\cos(\beta) }$

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

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