From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
Answer:
D
Step-by-step explanation:
The Savannah has very limited resources because of its environment so plants need to conserve and save as much energy and water as they can
Answer:
(4;-1)
Step-by-step explanation:
A(-4;2)
B(-2;-1)
C(1;1)
D(-4;-1)
1.5 cups of cocoa for every 1 cup of milk
Answer:
4 or -4
Step-by-step explanation:
Y is directly proportional to x^2 means there is a constant, k, such that y=kx^2.
We are given y=8 when x=2. This information will allow us to find k in the equation y=kx^2.
8=k(2)^2
8=k(4)
This implies k=2 since 2(4)=8.
So the equation for any pair (x,y) is y=2x^2.
We want to find x when y=32.
32=2x^2
32/2=2x^2/2
16=x^2
This implies x=4 or -4.
