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2 years ago

9sin(2x) sin (x) = 9cos(x)

Mathematics

1 answer:

nikdorinn [45]2 years ago

8 0

Answer:

$\sin(2x) = 2 \sin(x) \cos(x) \\ 9( 2 \sin(x) \cos(x) ) \sin(x) = 9 \cos(x) \\ 18 { \sin}^{2} (x)9 \cos(x) - 9 \cos(x) = 0 \\ 9 \cos(x) (2{ \sin}^{2} (x) - 1) = 0 \\ 9 \cos(x) = 0 \: or \: 2{ \sin}^{2} (x) - 1 = 0 \\ \sin(x) = \pm \frac{1}{ \sqrt{2} } \\ \cos(x) = 0 \\ x = { \cos}^{ - 1} (0) \\ x = \frac{ \pi}{2} = 90 \degree \\ x = \frac{ \pi}{2} + 2\pi \: n \: \forall \: n \: \in \: \Z \\ = 90 \degree + 360\degree\: n \: \forall \: n \: \in \: \Z \\ = \pm\frac{ \pi}{4} \pm2\pi \: n \: \forall \: n \: \in \: \Z \\ x = \pm45\degree \pm 360\degree\: n \: \forall \: n \: \in \: \Z$

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For a parallelogram with a long side that is 4 times the length of its short side find the area if the height from the long side

Zielflug [23.3K]

9514 1404 393

Answer:

c. 1150 square units

Step-by-step explanation:

The sum of the two side lengths is half the perimeter, so is 125/2 = 62.5 units. The long side is 4/5 of that, so is 50 units.

The area is the product of the long side and the height to the long side:

A = bh

A = (50 units)(23 units) = 1150 units²

<em>Additional comment</em>

This geometry is impossible, because the height from the long side cannot be more than the length of the short side. Here, the short side is 12.5 units, so it is not possible for the height to be 23 units.

If the height is measured from the short side, then the area is 287.5 square units.

5 0

3 years ago

the earth rotates about its axis once every 23 hours, 56 minutes and 4 seconds. Approximate the number of radians the earth rota

marishachu [46]

Answer:

$\frac{\pi}{43082}\text{ radians per second}$

Step-by-step explanation:

Given,

Time taken in one rotation of earth = 23 hours, 56 minutes and 4 seconds.

Since, 1 minute = 60 seconds and 1 hour = 3600 seconds,

⇒ Time taken in one rotation of earth = (23 × 3600 + 56 × 60 + 4) seconds

= 86164 seconds,

Now, the number of radians in one rotation = 2π,

That is, 86164 seconds = 2π radians

$\implies 1\text{ second }=\frac{2\pi}{86164}=\frac{\pi}{43082}\text{ radians}$

Hence, the number of radians in one second is $\frac{\pi}{43082}$

4 0

3 years ago

Write 108.92 in expanded form

Kitty [74]

Sorry if my writing is sloppy

5 0

3 years ago

A veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses

Licemer1 [7]

Answer:

Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

Step-by-step explanation:

We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.

So, firstly according to Central limit theorem the z score probability distribution for sample means is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = average age of the random sample of horses with colic = 12 yrs

$\mu$ = average age of all horses seen at the veterinary clinic = 10 yrs

$\sigma$ = standard deviation of all horses coming to the veterinary clinic = 8 yrs

n = sample of horses = 60

So, probability that a sample mean is 12 or larger for a sample from the horse population is given by = P( $\bar X$ $\geq$ 12)

P( $\bar X$ $\geq$ 12) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{12-10}{\frac{8}{\sqrt{60} } }$ ) = P(Z $\geq$ 1.94) = 1 - P(Z < 1.94)

= 1 - 0.97381 = 0.0262

Therefore, probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

4 0

3 years ago

If EFGH is a trapezoid, find its perimeter.

Serjik [45]

40.5
Trust me i did it and got it right!! if its wrong lmk and i can explain it for u

5 0

3 years ago