Take m = 50 , n=12. using matlab's linspace define t to be the m-vector corresponding to linearly spaced grid points from 0 to 1. using mathlab vander and fliplr define a to be the m*n matrix associated with least squares fitting on this grid by a polynomial of defree n-1
f(x) = height = 64 - 16x^2 = 0.
16x^2 = 64
x^2 = 4
x = 2, -2.
the zero x = 2 means that the height after time 2 is 0. this corresponds to the time of the rock hitting the ground.
the -2 can be ignored.
19 in 1 second
divide both sides by 2
one blueberry pie = $7
one pumpkin pie = $16
since there are two variables in this problem - the cost of blueberry pie and the cost of pumpkin pie, we can set up a system of equations to solve. since brandy sold 6 blueberry pies and 4 pumpkin pies for $106, our first equation is: 6b + 4p = 106.
molly sold 6 blueberry and 3 pumpkin for $90, so the second equation is: 6b + 3p = $90.
we can use elimination to add the two equations together and eliminate one variable while we solve for the other:
6b + 4p = 106
6b + 3p = 90
in order to eliminate a variable, you can multiply the first equation by -1:
-1(6b + 4p = 106) = -6b - 4p = -106
add 6b + 3p = 90
-p = -16, so p = 16
now, solve for b: 6b + 3(16) = 106 or 6b + 48 = 90
subtract 48 from both sides: 6b + 48 - 48 = 90-48
divide by 6: 6b/6 = 42/6
solve for b: b = 7
the correct answer is $81.28
in order to find this, we simply treat the word of as a multiplication symbol.
0.8% of 125% of $8128
now change the percentages to decimals
0.008 * 1.25 * 8128 = 81.28