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LuckyWell [14K]
3 years ago
10

Ira went to the movies with $35.91 in

Mathematics
2 answers:
svetlana [45]3 years ago
6 0

Answer:

$13.36

Step-by-step explanation:

12.5+6.25+3.8=22.55

35.91-22.55= 13.36

EleoNora [17]3 years ago
4 0
The answer is $13.36
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Let the smaller of the two numbers be x. Therefore the larger number is 1 bigger, x+1.

x + (x + 1) = 59
We can solve this equation for x, which will be one of our two numbers.
2x + 1 = 59
2x = 58
x = 29
Now that we've found x, we can find x + 1. In this case, x + 1 = 29 + 1 = 30.
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Given that sectheta = -37/12 what is the value of cottheta for pi/2 < theta< pi?
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Answer:

cotg(\theta) = -\frac{12}{35}

Step-by-step explanation:

The cotangent of theta is:

cotg(\theta) = \frac{\cos{\theta}}{\sin{\theta}}

For pi/2 < theta< pi

This means that the angle is in the second quadrant. In the second quadrant, the cosine is negative and the sine is positive. This means that the cotangent will be negative.

Secant:

sec(\theta) = \frac{1}{\cos{\theta}}

In this question

sec(\theta) = -\frac{37}{12}

So

-\frac{37}{12} = \frac{1}{\cos{\theta}}

Using cross multiplication

-37\cos{\theta} = 12

37\cos{\theta} = -12

\cos{\theta} = -\frac{12}{37}

Now we apply the following trigonometric identity:

\sin{\theta}^{2} + \cos{\theta}^{2} = 1

\sin{\theta}^{2} + (-\frac{12}{37})^{2} = 1

\sin{\theta}^{2} = 1 - (-\frac{12}{37})^{2}

\sin{\theta}^{2} = 1 - \frac{144}{1369}

\sin{\theta}^{2} = \frac{1369 - 144}{1369}

\sin{\theta} = \pm \sqrt{\frac{1225}{1369}}

Since the angle is in the second quadrant, the sine is positive.

\sin{\theta} = \frac{35}{37}

Finally, the cotangent:

cotg(\theta) = \frac{\cos{\theta}}{\sin{\theta}}

cotg(\theta) = \frac{-\frac{12}{37}}{\frac{35}{37}}

cotg(\theta) = -\frac{12}{35}

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