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Hunter-Best [27]
2 years ago
8

2(x+50)=16+4x What is x?

Mathematics
2 answers:
Taya2010 [7]2 years ago
5 0

Answer:

x=42

Step-by-step explanation:

Write the equation.

2(x+50)=16+4x

Spread the parentheses

2x+100=16+4x

Put variables on one side, numbers on the other.

2x-4x=16-100

Add/subtract/multiply/divide the variables with variables and numbers with numbers.

-2x=-84

Make x alone

-x=-42

Flip sides to make x positive

42=x

Leona [35]2 years ago
4 0
2x +100=16+4x
-2x. -2x
100=16+2x
-16. -16
84=2x
divide both sides
x=42
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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.

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

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

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

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

Add sin(x) to both sides:

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To solve this, we can use the unit circle.

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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.

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We have:

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Subtract sine from both sides:

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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 :)

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