The idea here is to take all three of those points and sub them into the general form of the quadratic equation and solve 3 equations by doing them 2 at a time. The general form is y = ax^2 + bx + c. If we set up the first two equations together using the x and y coordinates of the first 2 coordinates given, the system looks like this: 2 = a(-1)^2 + b(-1) + c
-1 = a(0)^2 +b(0) + c
Solving the second one gives you that c = -1, so we already know c. Solving the first equation we get 2 = a - b - 1, or 3 = a - b, subbing in a -1 for c. The next equation, using the last coordinate, looks like this: 5 = a(2)^2 + b(2) - 1 and
5 = 4a + 2b - 1 and 6 = 4a + 2b. Now we have these two equations left:
3 = a - b and 6 = 4a + 2b. Solve the first equation for b to get it in terms of a only: b = a - 3. Now sub in that b value for b in the second equation:
6 = 4a + 2(a - 3) and 6 = 6a - 6 and 12 = 6a so a = 2. Now we have a and c. Sub in the a value of 2 into b = a - 3 to get 3 = 2 - b. Solve for b to get that b = -1. So our equation in the end finally is y = 2x^2 - x - 1.
Answer:
a) r(t) = 0.783t radians
b) h(t) = 30cos(0.783*t) feet
Step-by-step explanation:
The situation is depicted in the picture attached
<h3>(see picture)
</h3>
Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply using the fact that 1 min = 60 seconds
4.7 radians __________ 60 seconds
r(t) radians ____________ t seconds
The height h(t) after t seconds is given by
h(t) = 30cos(r(t)) ===>
h(t) = 30cos(0.783*t) feet
Answer:
the final cost would be 123.05
915x100/100=
915/1×100/100=
91500/100=915
so B is the answer
Answer:
How much is the discount?
=$70
What is the final sale price?=$210
Step-by-step explanation:
$280 =100%
$x =25%
$280 x 25%=7000/100=<u>70</u>
<u>280-70=210</u>