![antoinetteee03](/avatars/21446.jpg)
antoinetteee03
29.04.2021 •
Mathematics
Part three of me suffering because of my math homework. ( last part)
Solved
Show answers
More tips
- H Health and Medicine What to Eat to Lose Weight?...
- S Society and Politics Will Japan become Russia s Military Enemy?...
- P Philosophy Is Everything We Strive for Eventually Achieved and Destroyed?...
- S Society and Politics Understanding Politics and Its Role in the Development of Civilization...
- P Philosophy Why Did God Create Man and Place Him in Obscurity?...
- S Society and Politics Skoptsy: Who They Are and How They Perform Castration?...
- O Other Childhood Fears: What Many of Us Experienced...
- P Philosophy What is Something for you?...
- H Health and Medicine Why Do Humans Have One Heart?...
- P Philosophy Unbelievable stories of encounters with otherworldly forces...
Answers on questions: Mathematics
- M Mathematics Use the number line below, where RS = 7y + 2, ST = 2y +6, and RT = 13y - 12 a. What is the value of y? b. Find RS, ST, and RT. R What is the value of y?...
- M Mathematics Change 15 2/9 to degrees, minutes, and seconds....
- M Mathematics Is 14 times 10 to the power of 8 in scientific notation?...
- M Mathematics Mrs. McAlister wrote the equation 10 t minus 4 t + 3 t = 8 on the board and asked students to write an equivalent equation. The table below shows the responses from...
- M Mathematics 120 = -5 (2m - 7) + 5 Multi - Step...
- M Mathematics There were 94,172 people at a football game, which digit is in the thousand place in this number...
- M Mathematics I need help with this please and thank you!...
- M Mathematics Plz somebody help me...
- M Mathematics 5(x^3)^2(-2x^4)^-3 Simplify and write with positive exponents...
- M Mathematics Please help I need all the steps...
Ответ:
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.