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At what x-values do the graphs of the functions y = cos 2x and y =3cos^2x-sin^2x intersect over the interval -pi

Answers

Answer 1

Answer:

To find:

The x-values at the intersection of the graphs of two functions.

Solution:

Two functions are:

$y=\cos2x\text{ and }y=3\cos^2x-\sin^2x$

The functions are equal at the intersection. So,

$\cos2x=3\cos^2x-\sin^2x$

The solutions of the above equation are the x-values of the intersection.

$\begin{gathered} \cos2x=3\cos^2x-\sin^2x \n \cos^2x-\sin^2x=3\cos^2x-\sin^2x \n 2\cos^2x=0 \n \cos^2x=0 \n \cos x=0 \end{gathered}$

The solution to the above equation is:

$x=(\pi)/(2)+2\pi n\text{ and }x=(3\pi)/(2)+2\pi n$

It is given that x lies between -pi and pi. So, the value of n = 0 for the first solution and n = 1 for the second solution. Therefore,

$x=(\pi)/(2)\text{ and }x=-(\pi)/(2)$

Thus, options A and B are correct.

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Find the value of x. Round to the nearest tenth.

Hey can you please help me posted picture of question

Answers

Shifting to right means subtracting the number from x.

So, shifting to right by 9 units means, subtracting 9 from x.

G(x) = F(x - 9)

G(x) = |x - 9|

So, option D is the correct answer

Can Someone please explain how to solve this. The directions say, "Solve the system by graphing. Then check your solution."

Answers

Try this suggested solution (see the attached picture, the answer is [-2;1]).

1 step to drow the graph required in the condition;

2 step to find intersection point (this is the A point);

3 step, check stage, to solve the system of two equations.

4 to compare the results in step 2 and step 3.

Need Help Fast!!!!!!!!!!!!!!!!!!

Answers

7.2, 3, 8.09, 2.22, 5.06, 2.5

Mr. Markle has a jar on his desk that contains 10 marbles shown. What is the likelihood that a red marble will be chosen?

Answers

10 percent chance should be the right answer

Answer:

10% or 1/10 Or very Low ..

Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite theequation in slope-intercept form.

Answers

Answer: See below

Step-by-step explanation:

The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula $m=(y_(2)-y_(1) )/(x_(2)-x_(1) )$ to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.

$m=(-1-(-3))/(2-(-3)) =(2)/(5)$

Now that we have the slope, we can fill out the point-slope equation.

y-(-3)=2/5(x-(-3))

y+6=2/5(x+3)

This is the point-slope form.

Now, we can distribute and solve to get slope-intercept form.

y+6=2/5x+6/5

y=2/5x-24/5

Final answer:

The equation of the line through the points (-3,-3) and (2,-1) can be found using point-slope form. It is y = (2/5)x - 9/5 in slope-intercept form.

Explanation:

To find the equation of a line using the point-slope form, we need to determine the slope of the line and use one of the given points to write the equation. Firstly, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the coordinates (-3, -3) and (2, -1) into the formula gives us m = (-1 - (-3)) / (2 - (-3)) = 2/5. Now, we can choose one of the points (for example, (-3, -3)) and use the point-slope form equation: y - y1 = m(x - x1). Substituting the values, we get y - (-3) = (2/5)(x - (-3)). Simplifying the equation yields y + 3 = (2/5)(x + 3), which is the equation of the line in point-slope form.

To rewrite the equation in slope-intercept form y = mx + b, we need to isolate the y variable. Distributing the (2/5) to (x + 3) in the point-slope form equation gives us y + 3 = (2/5)x + 6/5. Subtracting 3 from both sides gives us y = (2/5)x + 6/5 - 3. Simplifying further, the equation becomes y = (2/5)x - 9/5. Therefore, the equation of the line through (-3, -3) and (2, -1) in slope-intercept form is y = (2/5)x - 9/5.

Learn more about Equation of a line here:

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a trapezoids longer base is 4 times its shorter base. If the trapezoid has an area of 80 cm squared and a height of 8cm has what is the length of each base

Answers

Long One is 16
Short One is 4!!

A=base+base/2 * height

A=80

16+4/2 = 10

10 * 8 = 80!!

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An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the baggage compartment can be estimated by the least squares regression equation y=103+30x. Predict the weight of luggage for a flight with 86 passengers.

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