Write a solution to the equation x? = 75 two ways: using exponents using radicals
1 answer:
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Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:
Answer:
The Distance cover by boat in 2 hours and 15 minutes is 72 km
Step-by-step explanation:
Given as :
The Distance cover by boat = 128 kilometer
The time taken is 4 hours
As , Distance = Speed ×Time
So , Speed =
Or, Speed =
∴ Speed = 32 km per hour
Now, again The boat travel 2 hours and 15 minutes further with speed 32 kmph
So, Time2 = 2 +
Or, Time2 = 2 +
I.e Time2 = hours
Again , Distance = Speed ×Time
So , Distance = 32kmph × hours
I.e Distance = = 72 kilometer
Hence The Distance cover by boat in 2 hours and 15 minutes is 72 km Answer