Since ![[0,4]=[0,1]\cup(1,4]](https://tex.z-dn.net/?f=%5B0%2C4%5D%3D%5B0%2C1%5D%5Ccup%281%2C4%5D)
, we can rewrite the integral as
Now there is no ambiguity about the definition of f(t), because in each integral we are integrating a single part of its piecewise definition:
Both integrals are quite immediate: you only need to use the power rule
to get
![\displaystyle \int_0^11-3t^2\;dt = \left[t-t^3\right]_0^1,\quad \int_1^4 2t\; dt = \left[t^2\right]_1^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E11-3t%5E2%5C%3Bdt%20%3D%20%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%2C%5Cquad%20%5Cint_1%5E4%202t%5C%3B%20dt%20%3D%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4)
Now we only need to evaluate the antiderivatives:
![\left[t-t^3\right]_0^1 = 1-1^3=0,\quad \left[t^2\right]_1^4 = 4^2-1^2=15](https://tex.z-dn.net/?f=%5Cleft%5Bt-t%5E3%5Cright%5D_0%5E1%20%3D%201-1%5E3%3D0%2C%5Cquad%20%5Cleft%5Bt%5E2%5Cright%5D_1%5E4%20%3D%204%5E2-1%5E2%3D15)
So, the final answer is 15.
Answer:
B & D
Step-by-step explanation:
We use percents in decimal form to multiply it with the price. We convert percents into decimals by dividing the percent number by 100. For example, 78% divided by 100 becomes 0.78.
There are two ways to look at it:
- For finding the price we pay during a sale, we focus on the percent we pay. If 22% off is the sale, then we spend 78% or 100-22=78. If 20% off is the sale, then we pay 80% or 0.80. Multiply that by x an unknown price and we have 0.8x.
- We can find the percent off by multiplying the price by the percent conversion. So 20% is 0.20. Then subtract it from the original price to find the leftover that we pay. This is x-0.2x.
B. Is correct I think. Hope this helped you
Answer:
W = 15/4 ft . ib
Step-by-step explanation:
Force = 10ib
According to hooked law, f(x) = kx
x = 4inches = 4/12 ft
x= 1/3ft
f(x) = 1/3k
10 = 1/3k
k = 30 ib/ft
f(x) = 30x
Workdone = integral of f(x) with its limit
6 inches = 6/12 ft
= 1/2ft
W = integral(1/2 to 0) of 30x
W = 15x^2(1/2 to 0)
W = 15(1/2)^2 - 15(0)^2
W = 15(1/4) - 0
W = 15/4 ft. Ib
You're having some formatting problems. You may have to do without the special symbols.
<span>Christopher bought a new watch at the store when they were having a 20% off sale.
</span><span>If the regular price of the watch was $48, what did Chris have to pay after the discount was applied?
Let w represent the cost of the watch. Then the discounted price would be (1.00-0.20)($48) = 0.8($48) = $38.40 (answer)</span>
