The formula for the average value of a function is
where b is the upper bound and a is the lower. For us, this formula will be filled in accordingly.
. We will integrate that now:
![\frac{1}{2}[ \frac{2x^3}{3}+3x]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%20%5Cfrac%7B2x%5E3%7D%7B3%7D%2B3x%5D%20%20)
from 0 to 2. Filling in our upper and lower bounds we have
![\frac{1}{2}[( \frac{2(2^3)}{3}+3(2))-0]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%28%20%5Cfrac%7B2%282%5E3%29%7D%7B3%7D%2B3%282%29%29-0%5D%20%20)
which simplifies to
and
which is 17/3 or 5.667
Answer:
Present age
Son: 15
Father: 45
Step-by-step explanation:
Remark
Thank you for the translation. Without it, the problem would be impossible -- at least for me.
Givens
Let the present age of the father = x
Let the present age of the son = y
Solution
x + y = 60
How many years will pass? You could say it's z.
x + z = y When z years pass, the son will be his father's present age.
x + z + y + z = 120 when z is added to both their current ages, the result is 120 Collect like terms
x + y + 2z = 120
<u>x + y = 60 </u> Subtract The very first equation
2z = 60 Divide by 2
z = 60/2 30 years have passed.
z = 30
x + z = y
x + 30 = y Substitute x + 30 for the present y value (the father).
x + x + 30 = 60
2x = 30
x = 15
x + y = 60
15 + y = 60
y = 60 - 15
y = 45
So the son's age right now is 15
The father's age right now is 45
The number of hours required for 3 tractors to plow the field is 2.4 hours
<em><u>Solution:</u></em>
Given that 5 tractors can plow a field in 4 hours
We have to find out number of hours required for 3 tractors to plow the field
5 tractors can plow a field in 4 hours, So time taken for 1 tractor
<em><u>So time taken for 3 tractors is given as:</u></em>
time taken for 3 tractor = time taken for 1 tractor x 3
So number of hours required for 3 tractors to plow the field is 2.4 hours
36000 x 10 = 360000 and 36000/10 = 3600
