Please help me :(
1 answer:
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All of these equations will be set up as: h(t) = +v₀t + h₀ where g represents gravity, v₀ represents initial velocity, and h₀ represents initial height. When working with ft/sec, g = 32. So, -g/2 = -16
1a) Length of time to reach its maximum height means you are looking for the x-value of the vertex (aka Axis Of Symmetry).
h(t) = -16t² + 160t
AOS: x = =
= 5
Answer: 5 sec
1b) Length of time to fall to the ground means you are looking for the x-intercept when height (y-value) = 0.
h(t) = -16t² + 160t
0 = -16t² + 160t
0 = -16t(t - 10)
0 = -16t 0 = t - 10
t = 0 t = 10
t = 0 is when it started, t = 10 is when fell to the ground.
Answer: 10 sec
2c) Same concept as 1a
h(t) = -16t² + 288t
AOS: x = =
= 9
Answer: 9 sec
2d) Same concept as 1b
h(t) = -16t² + 288t
0 = -16t² + 288t
0 = -16t(t - 18)
0 = -16t 0 = t - 18
t = 0 t = 18
Answer: 18 sec
3e) Same concept as 1a
h(t) = -16t² + 352t
AOS: x = =
= 11
Answer: 11 sec
3f) Same concept as 1b
h(t) = -16t² + 352t
0 = -16t² + 352t
0 = -16t(t - 22)
0 = -16t 0 = t - 22
t = 0 t = 22
Answer: 22 sec
Answer:
The function that represents the mass of the sample after t days is .
The percentage rate of change per hour is of -2.46%.
Step-by-step explanation:
Exponential amount of decay:
The exponential amount of decay for an amount of a substance after t days is given by:
In which A(0) is the initial amount, and r is the decay rate, as a decimal.
Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.
This means, respectively, that
So
The function that represents the mass of the sample after t days is .
Hourly rate of change:
Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So
-59%/24 = -2.46%
The percentage rate of change per hour is of -2.46%.