Dominic goes jogging every morning. If m represents the number of miles he jogs each day, which expression represents the total
2 answers:
Answer:
.
Step-by-step explanation:
Given : Dominic goes jogging every morning.
To Find: If m represents the number of miles he jogs each day, which expression represents the total number of miles he jogs in a week?
Solution:
Let m be the miles he jogs each day
No. of days in a week = 7
He jogs in 1 day = m miles
So, he jogs in 7 days =
Let t denotes the total number of miles he jogs in a week
So, he jogs in 7 days=
Hence the expression represents the total number of miles he jogs in a week is .
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Answer: y = x + 1
Step-by-step explanation:
First, we will find the slope. The slope of perpendicular lines are negative reciprocals.
In this case, the first slope is 2. The negative of 2 is -2, and the reciprocal of -2 is .
Now, we will plug in this new slope, the point given, and solve for the <em>b</em>, or the y-intercept.
y = <em>m</em>x + <em>b</em>
(-1) = ()(4) + <em>b</em>
-1 = -2 + <em>b</em>
1 = <em>b</em>
Lastly, we will write our equation.
y = <em>m</em>x + <em>b</em>
y = x + 1
The line is y = x + 1, or y = 1 -
.
Part A:
The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:
and
are points on the function
You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
Part B:
In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.
It is 25 times greater. This is because is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.