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tester [92]
1 year ago
10

Find Sin (BAC+30) 80POINTS

Mathematics
2 answers:
gogolik [260]1 year ago
8 0

sin<BAC

  • P/H
  • 16/20

cos<BAC

  • B/H
  • 12/20

NOw

  • sin(<BAC+30)
  • sin<BAC×cos30+cos<BACsin30
  • 16/20(√3/2)+12/20(1/2)
  • 2/5√3+3/10
Ann [662]1 year ago
3 0

Answer:

\dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}

Step-by-step explanation:

<u>Trigonometric Identities</u>

\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos (\angle BAC)=\dfrac{12}{20}
  • \sin (\angle BAC)=\dfrac{16}{20}

<u>Angles</u>

\sin (30^{\circ})=\dfrac{1}{2}

\cos (30^{\circ})=\dfrac{\sqrt{3}}{2}

Therefore, using the trig identities and ratios:

\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}

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Answer:

Volume of the cube = (2n6)³

Step-by-step explanation:

Volume of a cube = L*B*H

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Volume of the cube = (2n6)³

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Answer:

The approximate monthly rate of growth is 1.24%

Step-by-step explanation:

we have the future value formula

F=P(1+r)^t

we have

r=16\%=16/100=0.16 ----> annual interest rate

so

F=P(1+0.16)^t

F=P(1.16)^t

Find the approximate monthly rate of growth

Remember that

1\ year=12\ months

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Divide the number of periods t by 12

F=P(1.16)^{\frac{t}{12}}

Applying power rules property

F=P(1.16^\frac{1}{12})^t

F=P(1.0124)^t}

1.0124-1=0.0124

Convert to percentage

0.0124*100=1.24\%

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3 years ago
The average time a subscriber spends reading The Wall Street Journal is 49 minutes (The Wall Street Journal Subscriber Study). A
erica [24]

Answer:

P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)

And we can find the probability with the complement rule and the normal standard distirbution and we got:

P(z>0.6875)=1-P(z

Step-by-step explanation:

Let X the random variable that represent the time spent reading of a population, and for this case we know the distribution for X is given by:

X \sim N(49,16)  

Where \mu=49 and \sigma=16

We are interested on this probability

P(X>60)

And we can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

Using this formula we got:

P(X>60)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-49}{16})=P(z>0.6875)

And we can find the probability with the complement rule and the normal standard distirbution and we got:

P(z>0.6875)=1-P(z

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3 years ago
X=4y-5<br> 2x+3y=23<br> Solve using the substitution method
jenyasd209 [6]

Answer:

x =7, y = 3

Step-by-step explanation:

We substitute the value of x in terms of y (given) into the equation.

Then we solve for y and plug in the value of y back into the equation for the value of x to find x.

3 0
3 years ago
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