Jane and jill want their mom to ride the rollercoaster with them, but she thinks it will be too fast. she asks the girls to find out how fast the rollercoaster will be travelling. they find out that the speed of the rollercoaster, in miles per hour, is modeled by the function g(x) = x4 − 4x2 + 7x − 8, where x is time measured in seconds. how fast is the rollercoaster travelling at 2 seconds?

6 miles per hour

Step-by-step explanation:

Given the function  

It tells us the rate (speed) in miles per hour of the roller coaster at a time instant (x is the time).

If we want to find speed of roller coaster at 5 seconds, we will substitute 5 into x and find the value of g(x). that is the speed.

Similarly, in this problem we want the speed of the rollercoaster at time = 2 seconds, so we plug in 2 into x and find g(x), the speed. Shown below:

Hence, at 2 seconds, the roller coaster is going at 6 miles per hour

its an acute right triangle

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.