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2 years ago

PLS HELP ASAP! WILL MARK BRAINLIEST sin ∠A = 3/5 4/5 3/4 5/4

Mathematics

1 answer:

Dafna11 [192]2 years ago

5 0

Answer:

3/5

Step-by-step explanation:

sohcahtoa

since we're finding sine, we need the opposite and hypotenuse.

opposite of <A=3, hyp of <A=5.

opp comes before hyp in "soh", so sin<A=3/5

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Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

4 0

2 years ago

The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2.

mamaluj [8]

Answer:

The amount that Obi initially had was £20

Step-by-step explanation:

Let

x ----> amount that Obi initially has

y ----> amount that Rudy has

we know that

$\frac{x}{y} =\frac{5}{2}$

$x=2.5y$ ----> equation A

$x-20=y-8$

$y=x-20+8$

$y=x-12$ ----> equation B

Solve the system by substitution

substitute equation A in equation B

$y=(2.5y)-12$

solve for y

$2.5y-y=12\\1.5y=12\\y=8$

Find the value of x

$x=2.5(8)=20$

therefore

The amount that Obi initially had was £20

4 0

3 years ago

Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace

joja [24]

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean $\mu$ and default $\sigma$ , then the mean take seriously given as the straight line with a z score given by the confidence interval

$\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\$

Using formula:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

$P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)$

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

$=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z$

the required probability: $P(z>0.8349)=1-P(z$

4 0

2 years ago

Drag each function to the correct location on the table. Not all labels will be used.

nevsk [136]

The next one is 4th degree, so z to the fourth

6 0

3 years ago

Read 2 more answers

Two towns, Ancaster and Dundas, are 4 km and 6 km, respectively, from an old railroad line that has been made into a bike trail.

serg [7]

Okay, so first you draw a picture and let x be the distance from point D to the rest stop. Then the distance from point to the rest stop is 8 - x

You know that the length of the new trail is y + z, where y is the distance from Ancaster to the rest stop and z is the distance from Dundas to the rest stop.

Now by the Pythagorean theorem, y^2 = 4^2 + x^2 and z^2 = 6^2 + (8 - x) ^2

So take square roots of these, add them, and minimize.

Note: I am assuming the path is perfectly straight, otherwise this approach fails.

8 0

2 years ago