37 goes into 6 by=6.2 times
Answer:
4 x^(3/2) + 5x -32
Step-by-step explanation:
This problem involves definite integration (anti-derivatives).
If dy/dx = 6x^(1/2) - 5, then dy = 6x^(1/2)dx - 5dx.
(1/2) + 1
This integrates to y = 6x
----------------
(1/2) + 1 x^(3/2)
= 6 ------------ + C
3/2
or: 4 x^(3/2) + C
and the ∫5dx term integrates to 5x + C.
The overall integral is:
4 x^(3/2) + C + 5x + C. better expressed with just one C:
4 x^(3/2) + 5x + C
We are told that the curve represented by this function goes thru (4, 20).
This means that when x = 4, y = 20, and this info enables us to find the value of the constant of integration C:
20 = 4 · 4^(3/2) + 5·4 + C, or:
20 = 4 (8) + 20 + C
Then 0 = 32 + C, and so C = -32.
The equation of the curve is thus 4 x^(3/2) + 5x -32
(1/2 + 1)
Answer:
for cycling, time is 1.5 hours
for hogging time is 0.5 hour.
Step-by-step explanation:
speed of cycling = 30 km/h
speed of jogging = 8 km/h
total time = 2 hrs
total distance, D = 49 km
Let the time for cycling is t, so that time time for jogging is 2 - t .
distance = speed x time
49 = 30 x t + 8 (2 - t)
49 = 30 t + 16 - 8 t
33 = 22 t
t = 1.5 hour
So, time for cycling is 1.5 hours and time for jogging s 0.5 hr.
P = 2 ( 1 + w ) for 1
1 = 2 ( 1 + w )
Simplify
1 = 2w + 2
Subtract 2 from both sides
2w = -1
Divide by 2
2w = -1
/2 /2
w = -1/2