Hey guys, just got a few questions which I'm not too confident with.
1. |x+1| +x = |x-1|
2. When you are finding the volume of a curve that has been rotated about lets say the x axis, and the question specifically asks to use simpsons rule. Do you just find y2, input the values into the simpsons formula and then multiply it by pi?
3. What is the value of integral of [cos-1xdx]a-a where -1<=a<=1
4. How many times must a die be rolled so that the probability of rolling at least one size is greater than 95%?
For your first one, doing that algebraically would probably be gross. I'd take a graphical approach. If you draw the two sides of that equation on the same graph, just pick where they intersect and that's your answer! Drawing the one on the right is easy; the one on the left might be tricky; have a think!
Here is what you should get For your second one, yes
For your third one, do you mean you need to integrate \(\cos^{-1}{x}\)? Or just evaluate that anti-derivative in the brackets? Snap a pic of the original question?
Your fourth one, we could use binomial theorem and other such things; but let's just think of it simply. Every time we roll a dice, our probability of rolling NOT A SIX is \(\frac{5}{6}\). But as soon as we fail to do that, we have rolled a six. So, instead of considering how many times we need to roll to have a 95% chance of getting A six, let's just consider how many times we need to roll such that the probability of throwing NO SIXES becomes less than 5%! It's a complementary event
So we seek the lowest integer value of n such that:
By trial and error,
the answer is 17