Step-by-step explanation:
7x - 7 = 6x + 11
7x - 6x = 11 + 7
x = 18
Solution → x = 18
Answer: 18.66 miles per hour.
Step-by-step explanation:
The velocity of the Kayak can be written as the velocity of the kayak in still water plus the rate of the current.
If K is the velocity of the kajak, and C the velocity of the current, we have that:
When the kajak moves along with the current, for a given time T.
(K + C)*T = 10mi
when the kajak move against the current:
(K - C)*T = 4mi
now we can replace C by 8mph, and take the quotient of both equations:
((K + 8mph)*T)/(K - 8mph)*T)) = 10mi/4mi
(K + 8)/(K-8) = 10/4
K + 8 = (K- 8)*10/4
K + 8 = K*10/4 - 20
K*10/4 - K = K*6/4 = 20 + 8 = 28
K = 28*4/6 = 18.66
So the rate of the kajak is 18.66 miles per hour.
We're given
which immediately tells us that
In other words, swapping the limits of the integral negates its value.
Also,
The integral we want to compute is
which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is
Answer: Your answers ×=5 !