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Nataly_w [17]
2 years ago
6

What is the measure of

Mathematics
1 answer:
Kamila [148]2 years ago
6 0

Answer:

64.4

Step-by-step explanation:

In one of the trig formulas, it states    sin <a/A = sin<b/B = sin<c/C

So we have in this case:

sin(70)/12 = sin x/14           Note: x is just a variable for the angle <ABC

14(sin70)/12 = sin x

sin^-1(14(sin70)/12) = x

x=64.4

Your welcome, and comment if you have any questions! :D

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(24*32)/(2*3)
(768)/(6)
=128
I hope this helped you!!
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The vertex is a minimum point. The y value of the vertex is the lowest point it hits. The graph is going down, the vertex is the lowest point of it
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CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

y'=\cos^2(x)-\sin^2(x)

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

0=\cos^2(x)-\sin^2(x)

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

\cos(x)=-\sin(x)

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

5 0
3 years ago
Jose bought a bag of 6 oranges for $2.82. He also bought 5 pineapples. He gave the cashier $20 and received $1.43 change. How mu
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Your answer is: $3.15 each.

Here are the steps:

First, I added $2.82 and $1.43. Then, I subtracted the sum ($4.25) from $20. Lastly, I divided the difference($15.75) by five because there were five pineapples. Which gave me the answer: $3.15.
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3 years ago
A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn
allsm [11]
Salutations!

<span>A jar contains 2 red and 4 blue marbles. A marble is drawn from the jar. What is the probability that a red marble will be drawn?

So lets solve this! 

Probability is an event of chance; an occurrence of chance.

The probability that a red marble will be drawn is 2/6

Simply 2/6 which is 1/3

Thus, your answer is option C.

Hope I helped :D
</span>
5 0
3 years ago
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