To determine the number of those who joined the basketball camp this year, we just have to multiply the number of those who joined last year by the decimal equivalent of the percentage given. That is,
x = 88(1.25)
x = 110
Therefore, there are a total of 110 players for this years basketball camp.
![y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\ y''(0)=20\cdot0^3=0](https://tex.z-dn.net/?f=y%3Dx%5E5-3%5C%5C%20y%27%3D5x%5E4%5C%5C%5C%5C%205x%5E4%3D0%5C%5C%20x%3D0%5C%5C%200%5Cin%20%5B-2%2C1%5D%5C%5C%5C%5C%20y%27%27%3D20x%5E3%5C%5C%5C%5C%0Ay%27%27%280%29%3D20%5Ccdot0%5E3%3D0)
The value of the second derivative for
is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of
is always positive for
. That means at
there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval
![[-2,1]](https://tex.z-dn.net/?f=%5B-2%2C1%5D)
.
The function
is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.
29. A carpenter worked for 4 days to finish a repair job. She charged $825 for 15 hours plus $278 for materials. What is the carpenter's rate per hour?
Let’s start solving:
=> 825 dollars + 278 dollars = 1 103 dollars is the total payment a carpenter have received
=> 15 hours is the total hours he worked
=> 1 103 / 15 = 73.5 dollars per hour. This is already including the material or equipment fee.
We use FOIL method to multiply this out. First termsOuter termsInner termsLast terms Product = (3m3 * 3m3) + (3m3 * -1/2y) + (-1/2y * 3m3) + (-1/2y * -1/2y) Product = 9m6 - (3/2)m3y - (3/2)m3y + (1/4)y2 <span>Product = 9m6 - 3m3y + (1/4)y<span>2</span></span>
