Write the function d(t) = sqrt(90^2 + (90 − 16t)^2) as a composition. d(t) = f(g(t)), where g(t) = at2+bt+c is a quadratic function; �find a, b, c.
g(t) = 90^2 + (90 − 16t)^2 = 256t^2 - 2880t + 8100
f(t) = √t
d(t) = f(g(t)) = √g(t) = √(256t^2 - 2880t + 8100)
i got 16200 for the value of c because are you suppose to add 90^2 to 8100
right you are
my bad
To write the function d(t) = sqrt(90^2 + (90 − 16t)^2) as a composition of quadratic functions, d(t) = f(g(t)), we need to find a quadratic function g(t) = at^2 + bt + c that can be substituted into d(t).
Let's expand the expression inside the square root in d(t):
(90^2 + (90 − 16t)^2)
Simplifying this expression, we get:
8100 + 8100 - 2880t + 256t^2
Combining like terms, we have:
256t^2 - 2880t + 16200
Now we can see that this expression matches the form of a quadratic function g(t) = at^2 + bt + c. Comparing the coefficients, we can determine the values of a, b, and c:
a = 256
b = -2880
c = 16200
Therefore, the quadratic function that can be substituted into d(t) as a composition is:
g(t) = 256t^2 - 2880t + 16200