Determine the value of 0 acres

If sin theta = 2/5 and theta is in quadrant I, determine the following.

anzhelika [568]

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{2}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=adjacent\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ \pm\sqrt{5^2-2^2}=a\implies \pm\sqrt{21}=a\implies \stackrel{I~Quadrant}{+\sqrt{21}=a}$

recall that cosine is positive on the I Quadrant, so though we get a ± valid roots, only the positive one applies.

$\bf cos(\theta)=\cfrac{\stackrel{adjacent}{\sqrt{21}}}{\stackrel{hypotenuse}{5}} \\\\\\ tan(\theta)=\cfrac{\stackrel{opposite}{2}}{\stackrel{adjacent}{\sqrt{21}}} \qquad \qquad cot(\theta)=\cfrac{\stackrel{adjacent}{\sqrt{21}}}{\stackrel{opposite}{2}} \\\\\\ csc(\theta)=\cfrac{\stackrel{hypotenuse}{5}}{\stackrel{opposite}{2}} \qquad \qquad sec(\theta)=\cfrac{\stackrel{hypotenuse}{5}}{\stackrel{adjacent}{\sqrt{21}}}$

now, for tangent and secant, let's rationalize the denominator.

$\bf tan(\theta)\implies \cfrac{\stackrel{opposite}{2}}{\stackrel{adjacent}{\sqrt{21}}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies \cfrac{2\sqrt{21}}{21} \\\\\\ sec(\theta)\implies \cfrac{\stackrel{hypotenuse}{5}}{\stackrel{adjacent}{\sqrt{21}}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies \cfrac{5\sqrt{21}}{21}$

5 0

3 years ago

How can I solve this problem 2 1/2*4 1/5

vredina [299]

The easiest way to solve this problem is to make the fractions improper. 2 1/2 would be 5/2 and 4 1/5 would be 21/5.
Then you would multiply them straight across.
5*21= 105
2*5= 10
Afterward you would simplify.
105/10=10 1/2

5 0

3 years ago

Read 2 more answers

Rolling a fair Eight-sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard

kvv77 [185]

Answer:

a. The mean is 4.5 and the standard deviation is 0.3818.

b. 4.5

Step-by-step explanation:

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.

Mean of 4.5 and a standard deviation of 2.291.

This means that $\mu = 4.5, \sigma = 2.291$

a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.

By the Central Limit Theorem, the mean is 4.5 and the standard deviation is $s = \frac{2.291}{\sqrt{36}} = 0.3818$

The mean is 4.5 and the standard deviation is 0.3818.

b. The mean of the resulting distribution of the sample means is:________

By the Central Limit Theorem, 4.5.

4 0

3 years ago

A triangle with two congruent sides is always a(n)_______________ triangle.

LUCKY_DIMON [66]

Scalene triangle → Different length, therefore no congurent sides.
Isosceles triangle → Same length, therefore it has two congurent sides.
Equilateral triangle → All length are comparable, it has three congurent sides.
Right triangle → Measures 90°, in some cases, it has two congurent sides.

Congurent defination → Same shape and same size.

Answer → C) Isosceles triangle.

4 0

4 years ago

HELP ME FAST! PLEASE!

lisabon 2012 [21]

Answer:

0.3

Step-by-step explanation:

1dm=10cm

S0, 4dm would equal... 40cm

Thefore we would divide 12/40

This gives us a final result of 0.3

Hope this was helpfull!

3 0

4 years ago