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3 years ago

Solve the equation sin^2 x=3 cos ^2 x

Mathematics

2 answers:

larisa86 [58]3 years ago

6 0

Answer:

Step-by-step explanation:

Answer:

Explanation:

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Law Incorporation [45]3 years ago

6 0

$\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)=3cos^2(x)\implies sin^2(x)=3[1-sin^2(x)] \implies sin^2(x)=3-3sin^2(x) \\\\\\ sin^2(x)+3sin^2(x)=3\implies 4sin^2(x)=3\implies sin^2(x)=\cfrac{3}{4}$

$\bf sin(x)=\pm\sqrt{\cfrac{3}{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{2} \\\\\\ sin^{-1}[sin(x)]=sin^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies x= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}$

that is, on the interval [0, 2π].

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According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard devi

Mekhanik [1.2K]

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of $Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$ , in which $\mu$ is mean amount of inches of rain and $\sigma$ is the standard deviation.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean $\mu$ , standard deviation $\sigma$

n days:

This means that $s = \frac{\sigma}{\sqrt{n}}$

Applying the Central Limit Theorem to the z-score formula.

$Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

5 0

3 years ago

Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

Valentin [98]

Factoring by grouping usually pairs up the first 2 sets of expressions with the second 2 sets. Ours looks like this, then: $(x^3-9x^2)+(5x-45)=0$ . If we factor out the common x-squared in the first set of parenthesis, along with factoring out the common 5 in the second set, we get this: $x^2(x-9)+5(x-9)$ . Now the common expression that can be factored out is the (x-9). When we do that, here's what it looks like: $(x-9)(x^2+5)$ . I'm not sure how far you are going with this. You could set each of those equal to 0 and solve for x in each case. The first one is easy. If x - 9 = 0, then x = 9. The second one involves the imaginary i since x^2 = -5. In that case, $x=i \sqrt{5},-i \sqrt{5}$ . Hopefully, in what I have given you, you can find what you're looking for.

7 0

3 years ago

Can you help me solve x-1<-1 or 8x+9≥41

Elza [17]

For the first one:
x-1<-1
Add one on both sides.
x<0

For the second one:
8x+9≥41
Subtract nine on both sides.
8x+≥32
Divide by eight on both sides.
x≥4

HOPE THIS HELPS YOU! ^_^

3 0

3 years ago

Read 2 more answers

Your gross weekly salary is $800.00. Your federal income tax deduction is $53. The Social Security tax is 6.2%. The Medicare tax

lord [1]

Make an equation for this find the variables P and t and 200. Them plug the into an equation like y=mx+b.

6 0

3 years ago

Somebody help me lol

Lapatulllka [165]

Answer:

you subtract the exponents when dividing numbers with the same base

4 0

3 years ago