If the take the origin as the starting point of the ball, then the vertex would be (4,28) and the parabola would be facing downwards. Using the general form of the parabola which is (x-h)^2 = 4p(y-k) where h and k are taken from the coordinate of the vertex (h,k).
So, the equation would be, (x-4)^2)=4p(y-28). To determine 4p, we can substitute either of the two points: (0,0) or (0,8). The second coordinate is taken from the given that the ball covers a distance of 4 ft after it reaches a maximum height. The total distance traveled by the ball is twice that, which is 8 ft.
After substituting, 4p = -4/7. Plugging this into the equation and after expanding and simplifying, the equation of the ball's trajectory is:
y = (-4/7)x^2+14x
Answer:
69.6 miles per hour
Step-by-step explanation:
Length of the skid marks = 242 feet
The formula used for the velocity is
where, L is the length of skid marks in feet and the velocity obtain has the units of miles per hour.
By substituting the value
v = 69.6 miles per hour
Thus, the speed of the car at the time of accident is 69.6 miles per hour.
Answer:
37 more than the quotient of 24 and 8 = 24 ÷ 8 + 37
Step-by-step explanation:
24 ÷ 8 + 37
Order of Operations
3 + 37
Add
= 40
The expression is 24 ÷ 8 + 37
which means either
or
. The equation has no solution, since
is always bounded between -1 and 1. The second has one solution at
, and any number of complete revolutions will also satisfy this equation, so in general the solution would be
where
is any integer.
So you could choose
and
.
Sam's money will double faster.
The formula for compound interest is
A=p(1+r)ˣ, where A is the total amount in the account, p is the principal you invest, r is the interest rate as a decimal, and x is the amount of time.
If we want to represent the money being doubled, we would use 2p for A:
2p=p(1+0.09)ˣ
2p=p(1.09)ˣ
Divide both sides by p:
2p/p = p(1.09)ˣ/p
2 = 1.09ˣ
Using logarithms to solve this,
The formula for simple interest is
I = prt
If we want to find the amount of time to double the principal, this means the amount of interest would be equal to the principal invested:
p = p(0.09)t
Dividing both sides by p,
p/p = p(0.09)t/p
1 = 0.09t
Dividing both sides by 0.09,
1/0.09 = t
11.11 = t