Let's divide the shaded region into two areas:
area 1: x = 0 ---> x = 2
ares 2: x = 2 ---> x = 4
In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.
Area 1:
Area 2:
Therefore, the area of the shaded portion of the graph is
A = A1 + A2 = 5.34
It is answer choice B. Using the distributive property, -12x^3+15x^2-24x-6x^2+30x-42. Then combine like terms.
Answer:
Expected time is 15 hours for him to get to safety.
Step-by-step explanation:
We define X as the time that this miner would get to safety.
We define Y as the door he chooses initially.
P(Y= 1) = P(Y=2)=P(Y=3) = 1/3
We have E[X|Y=1] = 3
E[X|Y] = 5 hours + E[X}
E[X|Y] = 7 hours + E[X]
Then we have
E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])
We cross multiply
3*E[X] = (15 + 2E[x])
3E[X] - 2E[X] = 15
E[X] = 15
So the time it would take to get him to safety is 15 hours
Answer:
7.8
Step-by-step explanation:
First I will try 50. I got 127,550, so that was way too big.
Let me try a smaller number. How about 5. I got 155, so that was a bit too small.
Now I'll try 20. I got 8420. Looks like the number is between 5 and 20.
How about 7. I got 399.
Let me try 8. I got 584! That's really close. It's just a little too big.
I tried 7.5, and got 485.624. So close! Just a little higher.
Putting in 7.8 yields <u>543.192!</u> That's our answer.
Okay, so first you make f(x) = y and switch x and y. So the equation becomes:
x = y^2 - 16
The next step is to get y by itself. So first you add 16 to both sides:
x + 16 = y^2
Now you square root everything, so the final answer is going to be:
the square root of x + 4 = y
