Find the domain and range of the function f(x) = x -|2 cos x|

The graph of a quadratic function contains the points

masya89 [10]

Answer:

Shawn is correct.

Step-by-step explanation:

Let the quadratic function is g(x) = a(x - h)² + k

Here (h, k) is the vertex of the parabola.

Since this parabola passes through (0, 0), (1, 9) and (-1, 9), axis of symmetry is x = 0 and the vertex is (0, 0).

Therefore, equation of the parabola will be,

g(x) = a(x - 0)²+ 0

g(x) = ax²

for a point (1, 9) which lies on the graph,

9 = a(1)²

a = 9

g(x) = 9x² (here a > 1)

Therefore, f(x) is vertically stretched by a factor of 9 to form g(x).

Shawn is correct.

3 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bars(s).

kirza4 [7]

Answer:

(a)23 (b)90 (c)3

Step-by-step explanation:

The equation for the line of best fit for this situation is given as

$y=\frac{3}{10}x+8$

where x=average temperature in degrees

y=average number of hot dogs she sold,

(a) The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.

When x=50°

$y=\frac{3}{10}X50+8=15+8=23$

When the temperature is 50°, the expected number of hot dogs sold would be 23.

(b)If the vendor sold 35 hot dogs, the temperature is expected to be ___degrees.

If y=35

$35=\frac{3}{10}x+8\\35-8=\frac{3}{10}x\\27=\frac{3}{10}x$

Multiply both sides by 10/3

$27 X \frac{10}{3}= \frac{3}{10}x X \frac{10}{3}\\x=90^{0}$

If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

(c) Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

3 0

3 years ago

An electrician charges a $100 flat fee, plus $75 per hour to work on a house.

jek_recluse [69]

Answer:

y=75x+100

Step-by-step explanation:

8 0

2 years ago

In a list of 100 numbers , the fraction of numbers greater than 15 is (19/25) and the fraction of numbers less than 15 is (7/50)

Bingel [31]

19/25 * 100 = 1900/25 = 76 ....numbers greater then 15
7/50 * 100 = 700/50 = 14....numbers less then 15

100 - (76 + 14) = 100 - 90 = 10 <== numbers equal to 15

6 0

3 years ago

Please asap<br>for 10 points!

kari74 [83]

<h3>Given:</h3><h3>Large cone:</h3>

r= 8 cm
h= 20 cm

<h3>Small cone:</h3>

r= 4 cm
h= 10cm

r: radius
h: height

The volume of the frustum of the given cone.

<h3>Solution:</h3>

Frustum is a part of a cone formed by cutting off the top by a parallel plane.

$\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}$

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

formula.

$V= \frac{1}{3}×\pi×{4}^{2}×10$

$V= 167.5516082 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in the thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V= 167.55 \: {cm}^{3}}$

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.

$V= \frac{1}{3}×\pi×{8}^{2}×20$

$V= 1340.412866 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V=1340.41 \: {cm}^{3}}$

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.

$V= 1340.41-167.55$

$\large\boxed{V= 1172.86 \: {cm}^{3}}$

<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>

8 0

1 year ago