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maks197457 [2]
4 years ago
14

The figures above are similar find mn

Mathematics
1 answer:
notsponge [240]4 years ago
7 0
The figures above are similar<span>. </span>Find<span> the missing length. Show your work. . The sides will be in the same proportion L1/W1=L2/W2. Can you </span>find<span> ..</span>
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3 years ago
Ann read 105 pages in 3 hours. How many hours will it take her to read a 280 page chapter book?
S_A_V [24]

5 hours and 70 seconds

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4 years ago
How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)
Oxana [17]

Answer:

Make use of the fact that as long as \sin(\theta) \ne 0 and \cos(\theta) \ne 0:

\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}.

\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}.

\sin^{2}(\theta) + \cos^{2}(\theta) = 1.

Step-by-step explanation:

Assume that \sin(\theta) \ne 0 and \cos(\theta) \ne 0.

Make use of the fact that \tan(\theta) = (\sin(\theta)) / (\cos(\theta)) and \csc(\theta) = (1) / (\sin(\theta)) to rewrite the given expression as a combination of \sin(\theta) and \cos(\theta).

\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}.

Since \cos(\theta) \ne 0:

\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}.

Substitute this equality into the expression:

\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}.

By the Pythagorean identity, \sin^{2}(\theta) + \cos^{2}(\theta) = 1. Rearrange this identity to obtain:

\sin^{2}(\theta) = 1 - \cos^{2}(\theta).

Substitute this equality into the expression:

\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}.

Again, make use of the fact that \tan(\theta) = (\sin(\theta)) / (\cos(\theta)) to obtain the desired result:

\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}.

5 0
2 years ago
Marcie solved the following inequality, and her work is shown below:
Pie
So basically, all we have to do is change the signs when we multiply or divide by a negative so our answer is "When dividing by -8, she did not change the signs.


8 0
4 years ago
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