All categories

1 year ago

F(x)=cos(x). Find the x-intercepts of f(x) on [0, 2).

Mathematics

1 answer:

balu736 [363]1 year ago

3 0

The x-intercepts of the function where the function is given as y(x) = cos(x) are π/2 and 3π/2

<h3>What is the x-intercept of the function?</h3>

The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0

<h3>How to find the x-intercepts of the function?</h3>

The function is given as

f(x) = cos(x)

And the interval is given as

[0, 2)

The above means that we determine the value of x when the function f(x) equals 0

So, we have

cos(x) = 0

The above equation can be solved graphically

See attachment for the graph of the function f(x) = cos(x)

In the interval [0, 2), the graph crosses the x-axis at points x = π/2 and 3π/2

Hence, the x-intercepts of the function where the function is given as y(x) = cos(x) are π/2 and 3π/2

You might be interested in

Find the distance between the points (<br> -<br> 10,12) and (15,12).

Nitella [24]

The distance formula is:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

We are given two points in the form (x,y), so plug in the values to the distance formula:

$d= \sqrt{(-10-15)^2-(12-12)^2}$

Next we can simplify. We know that 12-12 is 0, so we can drop it from the equation, as it will not affect our answer. Also, we know that -10-15 is -25:

$d= \sqrt{(-25)^2}$

The square and square root cancel each other out leaving us with 25.

The answer is 25.

5 0

3 years ago

How are the surface area and volume of a rectangular prism related to each other?

MatroZZZ [7]

The surface area of a rectangular prism is equal to the volume of a rectangular prism on their cooresponding sides.

7 0

3 years ago

The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

Which of the following inequalities is equivalent to 1 ≥ x?

svp [43]

Answer:

x ≤ 1

Step-by-step explanation:

Swapping sides of the inequality requires reversing its sense.

If 1 is greater than x, then x is less than 1.

3 0

3 years ago

Read 2 more answers

Which relationships have the same constant of proportionality between yyy and xxx as the following table? xxx yyy 444 323232 777

Nataly [62]

Which relationships have the same constant of proportionality between yyy and xxx as the following table? xxx yyy 444 323232 777 565656 888 646464 Choose 3 answers: Choose 3 answers:

7 0

3 years ago

Read 2 more answers