Answer:
The rocket's maximum height will be 1424 feet.
It will reach that height in 4 seconds.
It will reach the ground in 8 seconds.
Step-by-step explanation:
One easy way to find the peak is to find the derivative and solve for zero:
h(t) = -16t² + 128t + 1680
To find the derivative of each term in that format, you simply multiply the coefficient by the exponent, and reduce the exponent by one. In the case of terms with no variable, they disappear. That gives us:
h'(t) = -32t + 128
This derivative describes the rate of change of h with respect to t, so to find the peak, we simply need to solve it for zero:
0 = -32t + 128
32t = 128
t = 4
So the maximum height occurs when t = 4. Let's plug it in to the original equation:
h(t) = -16t² + 128t + 1680
h(4) = -256 + 512 + 1680
h(4) = 1424
So the rocket's maxiumum height is 1424 feet.
And we've already answered the second question, it happens at 4 seconds.
Also, the amount of time going up will be the same as the amount of time going down, which means that it will reach the ground in twice that time, or 8 seconds.
Answer:
2y
Step-by-step explanation:
Simplifying
21x + -42y = 0
Solving
21x + -42y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '42y' to each side of the equation.
21x + -42y + 42y = 0 + 42y
Combine like terms: -42y + 42y = 0
21x + 0 = 0 + 42y
21x = 0 + 42y
Remove the zero:
21x = 42y
Divide each side by '21'.
x = 2y
Simplifying
x = 2y
Answer:
x = 15
LN and MO both equal 43
Step-by-step explanation:
LN and MO are diagonals in rectangle
Diagonals of a rectangle are congruent Hence, 4x - 17 = 2x + 13
Now we solve for x
4x - 17 = 2x + 13
Add 17 to both sides
4x = 2x + 30
Subtract 2x from both sides
2x = 30
Divide both sides by 2
x = 15
Now we want to find the values of LN and MO
To do so we substitute 15 for x in it's given expression ( note: because LN = MO we only need to do this process once )
LN = 4x - 17
Substitute 15 for x
4(15) - 17
Multiply
60 - 17
Subtract
LN and MO = 43
1. 0.87 is the same as 87/100
87/100
Answer:
242.
Step-by-step explanation:
C = 0.03 x 2 − 8 x + 700
When the marginal cost = $522 we have:
522 = 0.03 x 2 − 8 x + 700
0.03x^2 - 8x + 700 - 522 = 0
0.03x^2 - 8x + 178 = 0
Using the quadratic formula:
x = [ -(-8) +/- sqrt( 64 - 4 * 0.03 * 178)] / 0.06
= 8 +/- sqrt42.64 / 0.06
= 242 players.
