Alan

"When a long jumper leaves the ground at an an angle of 42.0 above the horizontal. He covers a distance of 9.00m. What is the take off speed of the jumper?"

Rearrange the second equation as y = 4 - x.  Substitute this into the first equation:

4 - x = x² - 3x + 4

This simplifies to. x² - 2x = 0

This factors as. x(x - 2) = 0, so x = 0 or x = 2

Substitute these back into y = 4 - x to find the corresponding values of y.

HT/ER = HA/EA, so HT = ER*HA/EA or HT = ER*(HE + EA)/EA 

I’ll leave you to fill in the numbers.

Perhaps this graph will help:

Yes, 1 is the correct answer:

Are you sure you have the limits written correctly in your second integral?

You are almost right asdf334, but you slipped up at the end! The probability of three heads is (1/2)³ = 1/8 (i.e. the same as getting no tails).

Correct Melody! In fact we have:

The population at the end of the n'th year is p = 15000*(1.065)ⁿ    (assuming 15000 is the population at the beginning of the first year).

You should be able to graph this on a graphing calculator.

The following should help:

If y(x) = atan(k/x) where k is a constant, then dy/dx = -k/(k² + x²)

For 1. note that \(|z| = |a+ib|=\sqrt{a^2+b^2}\)

For 2.