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tigry1 [53]
3 years ago
12

What is the approximate length of the third side of the triangle below?

Mathematics
2 answers:
Burka [1]3 years ago
5 0

Answer:

c

Step-by-step explanation:

8090 [49]3 years ago
4 0
You need the Law of Cosines here.  Let's call our given angle A, so the side across from it, the one we are looking to solve for, would be a.  The Law is as follows then: a^2=27^2+31^2-[2(27)(31)cos(75)].  We will simplify everything here at once to get a^2=729+961-433.26308.  a^2=1256.73692 so a = 35.5
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What is the difference between rates and proportions???
frez [133]
A rate often involves time:  e. g., 33 feet per second; also, we are finding the ratio of one type of measurement with respect to another:  distance and time.

A proportion is often the ratio of different measures of the same thing:

e. g.   5 apples
          ------------
           7 apples
6 0
3 years ago
What is the minimum value for the function shown in the graph?<br><br> Enter your answer in the box.
Fudgin [204]

The minimum value is the lowest point of a graphed line. The would be the bottom of the "U" shape.

Looking at the graph you can see that the bottom of the U is touching the horizontal line at x = -5.5, so this would be the minimum value.

The lowest part of the line is at -5.5

5 0
3 years ago
Read 2 more answers
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
2 years ago
What are some good hair dyes? that won’t damage my hair (comment too)
Mashutka [201]
Artic fox is pretty good!! It also smells really good :) I definitely recommend it
7 0
2 years ago
What is the slope of the graph y=-1
pochemuha
This is a horizontal line passing through  the point (0,-1).

Slope = zero.
4 0
3 years ago
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