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3 years ago

For what values of x∈[0,2π] does the graph of y=x+2cosx have a horizontal tangent?

Mathematics

1 answer:

Katen [24]3 years ago

3 0

Answer: x = pi/6 and x = pi/3.

Step-by-step explanation:

We have the function:

y = x + 2*cos(x)

It will have a horizontal tangent at the point where it's derivate is equal to zero.

Then first let's differentiate y.

y' = dy/dx = 1 - 2*sin(x).

Then we must find the value of x between 0 and 2*pi (or 0° and 360°)

y'(x) = 1 - 2*sin(x) = 0.

Let's solve that:

2*sin(x) = 1

sin(x) = 1/2.

We know that:

sin(30°) = 1/2.

and

Sin(120°) = 1/2

Then let's convert 30° into radians.

We know that:

pi = 180°.

Then:

pi/180° = 1.

30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6

120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.

Then the two values of x are: pi/6 and pi/3.

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Angles 1 and 2 are supplementary. 2 lines intersect to form angles 1 and 2. Which equation represents the relationship between t

mamaluj [8]

Answer:

$\angle 1 + \angle 2 = 180^o$

Step-by-step explanation:

Given

$\angle 1$ and $\angle 2$

Required

The relationship between them $\angle 1$ and $\angle 2$

From the question, we understand that $\angle 1$ and $\angle 2$ are supplementary

Supplementary angles add up to 180.

So, the relationship between $\angle 1$ and $\angle 2$ is:

$\angle 1 + \angle 2 = 180^o$

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3 years ago

1. A submarine is 40 meters below sea level. It goes up 12 meters, then goes down 30 meters. What is the submarine's new positio

expeople1 [14]

Answer:

Step-by-step explanation:

The submarine is below the sea level by 40 meters. Then, it goes up by 12. That means 40-12=28. The submarine goes 30m down again which means 28+30=58

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3 years ago

2. The path of a high diver is given by y = + (2x2 – 9x – 56), where y is the height of the diver

timofeeve [1]

Answer:

The diver will be 8 feet from the end of the board when he hits the water.

Step-by-step explanation:

The diver hits the water when y = 0.

To find the distance, we have to find the values of x when y = 0.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this problem, we have that:

$y = 2x^{2} - 9x - 56$

$2x^{2} - 9x - 56 = 0$

$a = 2, b = -9, c = -56$

Then

$\bigtriangleup = b^{2} - 4ac = (-9)^{2} - 4*2(-56) = 529$

$x_{1} = \frac{-(-9) + \sqrt{529}}{2*2} = 8$

$x_{2} = \frac{-(-9) - \sqrt{529}}{2*2} = -3.5$

It is a horizontal distance, so the answer is a positive value.

The diver will be 8 feet from the end of the board when he hits the water.

7 0

3 years ago

Solve for x.<br> x = [?]<br> 5x - 7/. 3x + 27

Tanzania [10]

Step-by-step explanation:

5x-7+3x+27=180

8x+20=180

8x=160

x=20°.

hope this helps you.

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