Answer:
0.375 feet-lb
Step-by-step explanation:
We have been given that the work required to stretch a spring 2 ft beyond its natural length is 6 ft-lb. We are asked to find the work needed to stretch the spring 6 in. beyond its natural length.
We can represent our given information as:
![6=\int\limits^2_0 {F(x)} \, dx](https://tex.z-dn.net/?f=6%3D%5Cint%5Climits%5E2_0%20%7BF%28x%29%7D%20%5C%2C%20dx)
We will use Hooke's Law to solve our given problem.
![F(x)=kx](https://tex.z-dn.net/?f=F%28x%29%3Dkx)
Substituting this value in our integral, we will get:
![6=\int\limits^2_0 {kx} \, dx](https://tex.z-dn.net/?f=6%3D%5Cint%5Climits%5E2_0%20%7Bkx%7D%20%5C%2C%20dx)
Using power rule, we will get:
![6=\left[ \frac{kx^2}{2} \right ]^2_0](https://tex.z-dn.net/?f=6%3D%5Cleft%5B%20%5Cfrac%7Bkx%5E2%7D%7B2%7D%20%5Cright%20%5D%5E2_0)
![6=\frac{k(2)^2}{2}-\frac{k(0)^2}{2}](https://tex.z-dn.net/?f=6%3D%5Cfrac%7Bk%282%29%5E2%7D%7B2%7D-%5Cfrac%7Bk%280%29%5E2%7D%7B2%7D)
![6=\frac{4k}{2}-0\\\\k=3](https://tex.z-dn.net/?f=6%3D%5Cfrac%7B4k%7D%7B2%7D-0%5C%5C%5C%5Ck%3D3)
We know that 6 inches is equal to 0.5 feet.
Work needed to stretch it beyond 6 inches beyond its natural length would be ![\int\limits^{0.5}_0 {kx} \, dx =\int\limits^{0.5}_0 {3x} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B0.5%7D_0%20%7Bkx%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5E%7B0.5%7D_0%20%7B3x%7D%20%5C%2C%20dx)
Using power rule, we will get:
![\int\limits^{0.5}_0 {3x} \, dx = \left [\frac{3x^2}{2}\right]^{0.5}_0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B0.5%7D_0%20%7B3x%7D%20%5C%2C%20dx%20%3D%20%5Cleft%20%5B%5Cfrac%7B3x%5E2%7D%7B2%7D%5Cright%5D%5E%7B0.5%7D_0)
![\frac{3(0.5)^2}{2}-\frac{3(0)^2}{2}\Rightarrow \frac{3(0.25)}{2}-0=\frac{0.75}{2}=0.375](https://tex.z-dn.net/?f=%5Cfrac%7B3%280.5%29%5E2%7D%7B2%7D-%5Cfrac%7B3%280%29%5E2%7D%7B2%7D%5CRightarrow%20%5Cfrac%7B3%280.25%29%7D%7B2%7D-0%3D%5Cfrac%7B0.75%7D%7B2%7D%3D0.375)
Therefore, 0.375 feet-lb work is needed to stretch it 6 in. beyond its natural length.
Answer:
Step-by-step explanation:
Answer: -15.5 or -31/2
Step-by-step explanation:
it may look weird but if that's what the equations says then your gonna do it.
-5(3/10) -> (5/1)(3/10) = 15/10 = -3/2 or -1.5
-1.5 - 14 = -15.5
![There!](https://tex.z-dn.net/?f=There%21)
<u>ANSWER:</u>
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If you need a explanation, just comment below! :)
![AnimeVines](https://tex.z-dn.net/?f=AnimeVines)
Answer:
D) 22/7
Step-by-step explanation:
22/7 = 3.14