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DIA [1.3K]
3 years ago
8

A bus travels 36 miles in 45 minutes. Enter the number of mi Es the bus travels in 60 minutes at this rate

Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer:

48

Step-by-step explanation:

\frac{36}{45} =\frac{x}{60} \\.8*60=x\\48=x

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(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

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or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
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cestrela7 [59]
2xy + 5 - 8 + 3xy - y +7 + 3y = 5xy - 8 + 2y + 12
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3 years ago
4/7 times a number minus 8.5 is no more than 11.5
mote1985 [20]
Good luck finding this answer 211
7 0
2 years ago
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Please help me with segment addition and midpoints
Tanya [424]

Answer:

3

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Since we know QR and RS are the same, we can add them together

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2 years ago
An optical inspection system is used to distinguish among different part types. The probability of a correct classification of a
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Answer: \mu=2.88\ \&\ \sigma^2=0.115

Step-by-step explanation:

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The formula to find the mean and variance for binomial distribution is given by :-

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Let the random variable X denote the number of parts that are correctly classified.

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Hence, the mean and variance of X are 2.88 and 0.115 respectively.

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