20 tulips. 2/3=20/30 when you multiply both the denominator and numerator by 10.
Answer:
vertex: (2,-18)
Step-by-step explanation:
y = ax² + bx + c
(-1,0) : a - b + c = 0 ...(1)
(5,0) : 25a +5b +c = 0 ...(2)
(0,-10): 0a + 0b + c = -10 c=-10
(1) x5: 5a - 5b + 5c = 0 ...(3)
(2)+(3): 30a + 6c = 0 30a = -6c = 60 a = 2
(1): 2 - b -10 = 0 b = -8
Equation: y = 2x² - 8x -10 = 2 (x² -4x +4) - 18 = 2(x-2)² -18
equation: y = a(x-h)²+k (h,k): vertex
vertex: (2,-18)
The given points are (4,8) & (9,-4)
slope of a line = <u>Y2 - Y1</u>
X2 - X1
====> <u>(-4) - 8</u> = <u>-12</u>
9 - 4 5
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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