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Klio2033 [76]
3 years ago
5

Solve for x. 3(x - 4) = 2x + 6 Α. Ο B. 2 C. 3.6 D. 10 E. 18

Mathematics
2 answers:
Zigmanuir [339]3 years ago
8 0
E. X=18 you can also just use Photomath or something if you need more help :)
LekaFEV [45]3 years ago
4 0
3(x - 4) = 3x - 12 (expand the brackets)
3x - 12 = 2x + 6
3x = 2x + 6 + 12 (put all of the integers on one side)
3x = 2x + 18 (simplify - collect like terms)
3x - 2x = 18 (put all of the unknowns on one side)
x = 18 (simplify - collect like terms)

Therefore, we know that x is equal to 18, and so the answer is E.
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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
What is the sum of the measure of the interior angles of an octagon
Afina-wow [57]

Answer:

1080°

Step-by-step explanation:

formula to find the sum of interior angles of a polygon is (n-2)×180

octagon has 8 sides so n=8

(8-2)×180

6×180

=1080°

6 0
3 years ago
Describe an animal adaptation and explain how it helps survival.
marin [14]

Answer and Step-by-step explanation:

Animal adaption for Birds.

Birds who live on a tropical island with large, hard shell nuts.

The birds have small beaks, but over time, their beaks become bigger, stronger, and sharper, so that it can break into the hard shell nuts, allowing them to eat the nuts.

<em><u>#teamtrees #WAP (Water And Plant)</u></em>

3 0
3 years ago
The measure of two angles of a triangle are 56 degrees and 39 degrees.find the measure of the third angle
8_murik_8 [283]

Answer:

85

Step-by-step explanation:

Angle 1: 56

Angle 2: 39

56+39=95

A triangles angles add up to 180 degrees.

180-95=85

Angle 3:85

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What is 8% of 200 estimated?
chubhunter [2.5K]

Answer:

16

Step-by-step explanation:

5 0
2 years ago
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