I think its b or c but my best guess would be b
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:
1. Number line 2
2. Number line 1
3. Number line 4
4. Number line 3
Step-by-step explanation:
1. x – 99 ≤ -104
Solving by adding +99 on both sides
x - 99 +99 ≤ -104 +99
x ≤ -5
Number line 2 represent x ≤ -5
2. x – 51 ≤ -43
Adding +51 on both sides
x -51 +51 ≤ -43 +51
x ≤ 8
Number line 1 represent x ≤ 8
3. 150 + x ≤ 144
Adding -150 on both sides
150 + x -150 ≤ 144 -150
x ≤ -6
Number line 4 represent x ≤ -6
4. 75 < 69 – x
Adding +x on both sides
75 + x < 69 -x +x
x < 69 -75
x < -6
Number line 3 represent x < -6
We know that that the water level is 3 feet below your deck. (-3)
When the tide goes out, the water level lowers 1 foot. (-1)
A storm surge comes in, the water level rises 2 feet. (+2)
New water level: -3-1+2= -4+2= -2
The new water level is 2 feet below the dock.
Mark as brainliest pls. Any concern or comment, talk to me.
