next three are n+2, n+4, and n+6
four consecutive odd have sum 56
n + n+2 + n+4 + n+6 = 56
4n + 12 = 56
4n = 44
n = 11
the numbers are 11, 13, 15, and 17
This can solved graphically, using algebraic manipulation or differential calculus.
Plotting the equation will generate a parabola. The vertex represents the point where the ball will reach the maximum height.
The vertex can be determined by completing the square
h = -16t2 + 45t + 5
h - 5 = -16(t2 - 45/16t)
h - 5 - 2025/64 = -16(t2 - 45/16t + 2025/1024)
(-1/16)(h - 2345/64) = (t - 45/32)^2
The vertex is
(45/32,2345/64) or (1.41,36.64)
The maximum height is 36.64 ft
Using calculus, taking the first derivative of the equation and equating to 0
dh/dt = 0 = -32t + 45
t = 45/32
Substituting this value to the equation
h = -16(45/32)^2 + 45(45/32) + 5
h = 36.64 ft
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Answer:
x = 18
Step-by-step explanation:
The angle vertically opposite (5x + 2) is also (5x + 2), then
(5x + 2) and (5x - 2) are same- side interior angles and sum to 180° , that is
5x + 2 + 5x - 2 = 180
10x = 180 ( divide both sides by 10 )
x = 18
Answer:
Step-by-step explanation:
slope m = (y₂ - y₁)/(x₂ - x₁)
= 6-6 / 8 - (-5) = 0/ 8+5 = o
Slope = o. ie the line is parallel to the x-axis.
Answer:
3/4
Step-by-step explanation:
54/72 simplified is the same as 3/4
