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Nat2105 [25]
3 years ago
14

The graph shows how much you and your friend each earn while mowing lawns

Mathematics
1 answer:
krek1111 [17]3 years ago
8 0

Answer:

what graph ? i do not see one

Step-by-step explanation:

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Consider the function f(x)=6sin(x-pi/8)+8. What transformation results in g(x)=6sin(x-7pi/16)+1?​
olga nikolaevna [1]

Answer: we have a vertical shift of 7 units down, and a horizontal shift of 5*pi/16 units to the right.

Step-by-step explanation:

First, let's define the transformations:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Here we have:

f(x) = 6*sin(x - pi/8) + 8

and the transformed function:

g(x) = 6*sin(x - (7/16)*pi) + 1

We can assume that the transformations are a vertical shift of A units, and an horizontal shift of B units, then we can write:

g(x) = f(x + B) + A

g(x) = 6*sin(x + B - pi/8) + (8 + A) = 6*sin(x - (7/16)*pi) + 1

Then we must have that:

(x + B - pi/8) = x -  (7/16)*pi

B - pi/8 = -(7/16)*pi

B = -(7/16)*pi + pi/8 =  -(7/16)*pi +2*pi/16 = (-7 + 2)*pi/16 = -5*pi/16

And we also must have that:

8 + A  = 1

A = 1 - 8 = -7

Then the transformation is:

g(x) = f(x - 5*pi/16) - 7

This means that we have a vertical shift of 7 units down, and a horizontal shift of 5*pi/16 units to the right.

3 0
3 years ago
Ava ate 5 wheat crackers, or 5% of the entire box. How many crackers were in the box?
mojhsa [17]
100 ;-; this is easy
7 0
3 years ago
Read 2 more answers
Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) a
devlian [24]

Answer:

The area under the function \int\limits^3_1 {9-x^2} \, dx \approx 7.25..

Step-by-step explanation:

We want to find the Riemann Sum for \int\limits^3_1 {9-x^2} \, dx with 4 sub-intervals, using right endpoints.

A Riemann Sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.

The Right Riemann Sum is given by:

\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)

where \Delta{x}=\frac{b-a}{n}

From the information given we know that a = 1, b = 3, n = 4.

Therefore, \Delta{x}=\frac{3-1}{4}=\frac{1}{2}

We need to divide the interval [1, 3] into 4 sub-intervals of length \Delta{x}=\frac{1}{2}:

\left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right], \left[2, \frac{5}{2}\right], \left[\frac{5}{2}, 3\right]

Now, we just evaluate the function at the right endpoints:

f\left(x_{1}\right)=f\left(\frac{3}{2}\right)=\frac{27}{4}=6.75

f\left(x_{2}\right)=f\left(2\right)=5=5

f\left(x_{3}\right)=f\left(\frac{5}{2}\right)=\frac{11}{4}=2.75

f\left(x_{4}\right)=f(b)=f\left(3\right)=0=0

Next, we use the Right Riemann Sum formula

\int\limits^3_1 {9-x^2} \, dx \approx \frac{1}{2}(6.75+5+2.75+0)=7.25

7 0
3 years ago
Uhm answer plz will give brainiest
Elina [12.6K]

Step-by-step explanation:

D=vt

where D=distance,v=velocity and t=time

Distance befoe stopped

D1=50.55mph *1.75 hr =88.46

Distance after stopped

D2 =45.2mi* 2.25 hr=101.7mi

The difference is:

101.7-88.46 = 13.24 mi

Then the answer would be:

Selena drove more miles after rest stop

And drove 13.24 mi more before before she stopped.

sorry I didn't see show your work. so took me a minute to write it all out for you.

7 0
2 years ago
Read 2 more answers
What is 24/8 in simplest form
Helen [10]
Its 3/1 divide both sides by 8 
6 0
3 years ago
Read 2 more answers
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