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4 years ago

If secθ = 13\5 and 270° < θ < 360°, then tanθ = _____. -12\5 -5\12 5\12 12\5

Mathematics

1 answer:

r-ruslan [8.4K]4 years ago

4 0

Answer:

tanΘ = - $\frac{12}{5}$

Step-by-step explanation:

Using the trigonometric identity

tan²Θ + 1 = sec²Θ, thus

tan²Θ + 1 = ( $\frac{13}{5}$ )² = $\frac{169}{25}$ ( subtract 1 from both sides )

tan²Θ = $\frac{144}{25}$ ( take the square root of both sides )

tanΘ = ± $\sqrt{\frac{144}{25} }$

Since 270 < Θ < 360 , that is the fourth quadrant where tan Θ < 0, thus

tanΘ = - $\frac{12}{5}$

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kiruha [24]

Answer:

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Step-by-step explanation:

At the beginning there was 1 penny. At the second day the amount of pennies under the pillow became 2.

The amount of pennies doubled each day. So the series is,

$1,2,4,8,16,32,.....$

This series is in geometric progression.

As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be,

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where,

a = initial term = 1,

r = common ratio = 2,

As we have find the number of days that would elapse before she has a total of more than 90 trillion, so

$\Rightarrow 90\times 10^{12}\le \dfrac{1(2^n-1)}{2-1}$

$\Rightarrow 90\times 10^{12}\le \dfrac{2^n-1}{1}$

$\Rightarrow 90\times 10^{12}\le 2^n-1$

$\Rightarrow 2^n\ge 90\times 10^{12}+1$

$\Rightarrow \log 2^n\ge \log (90\times 10^{12}+1)$

$\Rightarrow n\times \log 2\ge \log (90\times 10^{12}+1)$

$\Rightarrow n \ge \dfrac{\log (90\times 10^{12}+1)}{\log 2}$

$\Rightarrow n \ge 46.4$

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3 years ago

Triangle MNO is similar to triangle PRS. Find the measure of side PR. Round your

Fudgin [204]

Answer:

PR = 34.4

Step-by-step explanation:

x/54 = 7/11

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3 years ago

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Answer:

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Step-by-step explanation:

Assuming he takes equal number of quizzes weekly then having taken 24 quizzes within 4 weeks means for every week Carson took 24/4=6 quizzes per week.

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3 years ago

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statuscvo [17]

Answer:

2.41

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3 years ago