How many stuffed animals are on the scale
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Answer:
84 cups of water will leak out after 2 weeks
Step-by-step explanation:
* Lets how many how to change oz to cup
- One cup contains 8 oz
- We can use the ratio to solve this problem
- A hose is leaking water at a rate of 2 oz/h
- We need to find how many cups of water will leak out after 2 weeks
∵ The rate of the water leak out is 2 oz/hr
∵ 1 cup contains 8 oz
∴ 1 oz = cup
∴ 2 oz = 2 × =
=
cup
∴ The rate of the water leak out = cup/h
∵ 1 day = 24 hours
∵ 1 week = 7 days
∴ 1 week = 7 × 24 = 168 hours
∵ The number of hours in 1 week is 168
∴ The number of hours in 2 weeks = 168 × 2 = 336 hours
⇒ cups : hours
⇒ : 1
⇒ x : 336
- By using cross multiplication
∴ x = 336 ×
∴ x = 84
- x represents the number of cups of water leak out
<em>84 cups of water will leak out after 2 weeks</em>
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: