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Ad libitum [116K]
4 years ago
10

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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A leprechaun places a magic penny under a girls pillow. The next night there are 2 magic pennies under her pillow. The following
kiruha [24]

Answer:

<em>After </em><em>47</em><em> days she will have more than 90 trillion pennies.</em>

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,

S_n=\dfrac{a(r^n-1)}{r-1}

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

\Rightarrow n\approx 47


8 0
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

11x = 378

x = 34.4

7 0
3 years ago
Carson took a total of 24 quizzes over the course of 4 weeks. How many weeks of school will Carson have to attend this quarter b
erastovalidia [21]

Answer:

9 weeks

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.

With a target of 54 quizzes this quater and while maintaining 6 quizzes per week then Carson will take 54/6= 9 weeks to meet thw target.

Therefore, Carson needs 9 weeks this quater

7 0
4 years ago
Can someone helpp meeee
Lyrx [107]
You have to add all of them together for money
5 0
3 years ago
StartFraction 47 Over 39 EndFraction = StartFraction b Over 2 EndFraction
statuscvo [17]

Answer:

2.41

Step-by-step explanation:

Cross multiplication

47(2)=39b

94÷39=39b÷39

2.41=b

3 0
3 years ago
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