Julio spent $41 and now has no money left he had BLANK before his purchase. write the integer
1 answer:
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Answer:
Yes; at 1.75 s; 72.25 ft
Step-by-step explanation:
h = -16t² +68t
a = -16; b = 68; c = 0
The vertex h of a parabola is at
h = -b/(2a) and the maximum height is at
y = f(h)
1. Time to maximum height
2. Maximum height
3. Does the golf ball reach 70 ft?
Yes, it passes 70 ft on the way to its maximum height of 72.25 ft.
4. Time to 70 ft
-16t² + 68t = 70
-16t² + 68t - 70 = 0
8t² -34t + 35 = 0
( 4t -7) (2t - 5) = 0
4t - 7 = 0 2t - 5 = 0
4t = 7 2t = 5
t = 1.75 s t = 2.5 s
The golf ball reaches 70 ft at 1.75 s on the way up and 2.5 s on the way down.
The diagram below shows the path of your parabola.
The horizontal function is x(t) = 8·t
The vertical function is y(t) = -16·t² + 100
A) The answer is: it takes her 2.62 time units to reach the ground.
The time taken to move horizontally is equal to the time taken to move vertically from the cliff to the ground, therefore, we can set:
8·t = -16·t² + 100
and solve for t:
16·t² + 8·t - 100 = 0
4(4·t² + 2·t - 25) = 0
4·t² + 2·t - 25 = 0
t₁ = (-1 + √101) / 4 = 2.62
t₂ = (-1 - √101) / 4 = - 2.76
We cannot accept negative times, therefore the solution is t = 2.62 time-units.
B) The answer is: she lands 20.96 distance-units from the cliff.
In order to find the distance travelled, substitute the time taken found in point A into the equation of the horizontal movement (using the vertical one you would calculate the height of the cliff):
x(t) = 8·t
x(2.62) = 8 · 2.62 = 20.96
Hence, Lukalu lands 20.96 distance-units from the cliff.
The vertical function is y(t) = -16·t² + 100
A) The answer is: it takes her 2.62 time units to reach the ground.
The time taken to move horizontally is equal to the time taken to move vertically from the cliff to the ground, therefore, we can set:
8·t = -16·t² + 100
and solve for t:
16·t² + 8·t - 100 = 0
4(4·t² + 2·t - 25) = 0
4·t² + 2·t - 25 = 0
t₁ = (-1 + √101) / 4 = 2.62
t₂ = (-1 - √101) / 4 = - 2.76
We cannot accept negative times, therefore the solution is t = 2.62 time-units.
B) The answer is: she lands 20.96 distance-units from the cliff.
In order to find the distance travelled, substitute the time taken found in point A into the equation of the horizontal movement (using the vertical one you would calculate the height of the cliff):
x(t) = 8·t
x(2.62) = 8 · 2.62 = 20.96
Hence, Lukalu lands 20.96 distance-units from the cliff.