Question

Identify the slope of the asymptotes of 5(y -1)2 - 20(x - 1)2 =64.

The number of possible positive real zeros of f(x) = 3x4 - 12x3 + 25x2 is


The area of a parking lot is 805 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. At most 80 vehicles can park at one time. If the cost to park a car is $2.00 and the cost to park a bus is $6.00, how many buses should be in the lot to maximize income?

Answer 1

can someone help me out with these questions?

Answer 2

The first one:
5(y -1)^2 - 20(x - 1)^2 =64
[(y -1)^2]/(2^2) - (x - 1)^2 =3.2
So this is a hyperbola, with asymptotes y-1 = ±2(x-1) (since center (1,1)) --> Simplify

The number of possible positive real zeros of f(x) = 3x4 - 12x3 + 25x2
Set f(x) = 0
3x4 - 12x3 + 25x2 = 0
x^2 (3x^2 - 12x + 25) = 0
x = 0 or 3x^2 - 12x + 25 = 0
But 3x^2 - 12x + 25 = 0 doesn't have any roots (see attached diagram)
So The number of possible positive real zeros of f(x) = 3x4 - 12x3 + 25x2 is 0

Answer 3

thank you i was stuck on that forever

Answer 4

I'm having problems with the last one though... Cuz I get linear functions rather than other functions.... And then I can only get one answer for the derivative