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hammer [34]
3 years ago
5

Find a function of the form f(x) = a sin(bx − c) such that the graph of f matches the figure.

Mathematics
1 answer:
aliina [53]3 years ago
4 0

Answer:

y = 3sin(2x+pi)

Step-by-step explanation:

We know that a is equal to 3 because the distance from 3 to the midpoint 0 is 3

We also know that is a phase shift of pi/2 as that is where the new start of our sine function lands

We know there is a compression of 2 as our period has changed from 2pi to pi

So naturally we change pi/2 to pi since we put the 2 inside the parenthesis

Best of luck

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Car A's fuel efficiency is 34 miles per gallon of gasoline, and car B's fuel efficiency is 23 miles per gallon of gasoline. At t
Verdich [7]

Answer:

22 more gallons.

Step-by-step explanation:

Given:

Car A's fuel efficiency is 34 miles per gallon of gasoline.

Car B's fuel efficiency is 23 miles per gallon of gasoline.

Question asked:

At those rates, how many more gallons of gasoline would car B consume than car A on a 1,564 miles trip?

Solution:

<u>Car A's fuel efficiency is 34 miles per gallon of gasoline.</u>

<u>By unitary method:</u>

Car A can travel 34 miles in = 1 gallon

Car A can travel 1 mile in = \frac{1}{34} \ gallon

Car A can travel 1564 miles in = \frac{1}{34} \times1564=46\ gallons

<u>Car B's fuel efficiency is 23 miles per gallon of gasoline.</u>

Car B can travel 23 miles in = 1 gallon

Car B can travel 1 mile in = \frac{1}{23} \ gallon

Car B can travel 1564 mile in = \frac{1}{23} \times1564=68\ gallons

We found that for 1564 miles trip Car A consumes 46 gallons of gasoline while  Car B consumes 68 gallons of gasoline that means Car B consumes 68 - 46 = 22 gallons more gasoline than Car A.

Thus, Car B consumes 22 more gallons of gasoline than Car A consumes.

<u />

6 0
3 years ago
Solve the system of equations.
Xelga [282]

Answer:

  b.  x=1, y=2, z=3

Step-by-step explanation:

The system of equations ...

  • 3x +2y +z = 10
  • 9x -6y +z = 0
  • x -y -3z = -10

has solution (x, y, z) = (1, 2, 3) . . . . matches choice B.

_____

While it is convenient to solve this using a graphing calculator or web site, one can easily solve the system by hand.

Subtract the second equation from 3 times the first:

  3(3x +2y +z) -(9x -6y +z) = 3(10) -(0)

  12y + 2z = 30 . . . . simplify

Dividing this result by 2 gives ...

  6y +z = 15 . . . . . . [eq4]

Subtract 3 times the third equation from the first:

  (3x +2y +z) -3(x -y -3z) = (10) -3(-10)

  5y +10z = 40 . . . . simplify

  y + 2z = 8 . . . . . . . divide by 5 . . . . . [eq5]

The two equations [eq4] and [eq5] can be solved any of the ways you usually solve two equations in two variables. Here, we'll use the first equation to write an expression for z that we can substitute into the second equation.

  z = 15 -6y . . . . . subtract 6y from [eq4]

  y + 2(15 -6y) = 8 . . . . . substitute for z in [eq5]

  -11y +30 = 8 . . . . . simplify

  -11y = -22 . . . . . . . subtract 30

  y = 2 . . . . . . . . . . . divide by the coefficient of y

  z = 15 -6(2) = 3 . . . . substitute for y in our equation for z

Substituting these values for y and z into the third original equation gives ...

  x - 2 -3(3) = -10

  x -11 = -10 . . . . . . . . simplify

  x = 1 . . . . . . . . . . . . add 11

The solution to the above system of equations is (x, y, z) = (1, 2, 3).

_____

<em>Comment on the problem statement</em>

Math is generally unforgiving of imprecision. The given system of equations has no variable "z", and some other typos are apparently involved. That is why we rewrote the system to the equations shown above.

It is very easy to mistake z for 2, or g for 9, or o for 0, or 1 for 7. There are other confusions that are possible, as well. Letters I (eye) and l (ell) are easily confused, and may be confused with 1 (one) as well. Sometimes y and 4, or 4 and 9, can also be written so as to be difficult to tell apart. Great care must be taken when handwriting these symbols.

7 0
3 years ago
Expand the expression and combine like terms
____ [38]
But what is the expression, you have to tell me so I can do it.
4 0
3 years ago
This puzzle is relatively easy, I just posted here cause I wanted to see if how many people can solve it. I capitalized some of
aleksandrvk [35]

Answer:

4 minutes

Step-by-step explanation:

2 will cook together for 1 minute. and it will take an additional 2 minutes to cook the 3rd pancake.

6 0
3 years ago
a group of astronauts launched a model rocket from a platform. Its flight path is modeled by h= -4t^2+24t+13 where h is the heig
Eddi Din [679]

Answer:

6.5 seconds

Step-by-step explanation:

Keep in mind that when h=0, this is the same height for both when the model rocket takes off and lands, so when the rocket lands, time is positive. Thus:

h=-4t^2+24t+13\\\\0=-4t^2+24t+13\\\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\t=\frac{-24\pm\sqrt{24^2-4(-4)(13)}}{2(-4)}\\ \\t=\frac{-24\pm\sqrt{576+208}}{-8}\\\\t=\frac{-24\pm\sqrt{576+208}}{-8}\\\\t=\frac{-24\pm\sqrt{784}}{-8}\\\\t=\frac{-24\pm28}{-8}\\\\t=\frac{-24-28}{-8}\\ \\t=\frac{-52}{-8}\\ \\t=\frac{52}{8}\\\\t=6.5

So, the amount of seconds that the model rocket stayed above the ground since it left the platform is 6.5 seconds

5 0
2 years ago
Read 2 more answers
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