Answer:
- yes
- v(t) gives the instantaneous velocity at time t
(a) correct
(b) -48 ft/s
(c) -32 ft/s; -64 ft/s
(d) 9.257 s
(e) -296.216 ft/s
Step-by-step explanation:
You are given an equation of motion and asked to find velocity and time at different points in the motion. This requires you differentiate the position function to find velocity, and that you solve the position function to find the time at a particular position.
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<h3>(a)</h3>
The coin is "dropped", so is presumed to have no initial velocity. The initial height is given as 1371 feet. Putting these values into the given equation, you have ...
s(t) = -16t² +1371
The velocity is the derivative of this function:
v(t) = -32t
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<h3>(b)</h3>
The average velocity on an interval is the change in position divided by the change in time:
(s(2) -s(1))/(2 -1) = ((-16·2² +1371) -(-16·1² +1371))/1 = -16(4 -1) = -48 . . . ft/s
(Note: the average velocity for a quadratic position function is the velocity at the midpoint of the interval: v(1.5) = -32(1.5) = -48 . . . ft/s.)
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<h3>(c)</h3>
Use the velocity function you found in part (a) to determine the instantaneous velocity at the given times:
v(1) = -32(1) = -32 . . . ft/s
v(2) = -32(2) = -64 . . . ft/s
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<h3>(d)</h3>
The coin will reach the ground when s(t) = 0. Solving for t, we find ...
s(t) = 0
-16t² +1371 = 0
1371 = 16t²
t = √(1371/16) = (√1371)/4 ≈ 9.257 . . . . seconds
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<h3>(e)</h3>
The velocity at impact will be ...
v(√1371/4) = -32(√1371/4) = -8√1371 ≈ -296.216 . . . ft/s
go to this site
https://www.tiger-algebra.com/drill/1/x-3=1/2x/
Mike brought $15 and Hallie brought $45 to the movie
There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
The value of the variable that makes the equation a true statement is the solution to the equation.
We have to find how much money Mike and Hallie brought to the movie.
Let the money Brought by Mike be $ m and by Hallie be $ h.
Mike and hallie are going to a movie. together they bring $60 in cash
m + h = $ 60.............(1)
Hallie brings three times as much cash as mike does
h = 3 m.......... (2)
Pur the value of h from equation (2) in equation (1)
m + 3 m = $ 60
4 m = $ 60
m = $ 60/4
m = $ 15
put this value of m in equation (2)
h = 3(15)
h = $ 45
Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie
<u>Learn more about equation here:</u>
brainly.com/question/28052720<u> </u>
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Answer:
See answers below
Step-by-step explanation:
Problem 1)
Conditional: If two angles are supplementary, then their sum is 180 degrees
Truth value: True
Converse: If the sum of two angles is 180 degrees then the two angles are supplementary.
Truth value: True
Problem 2)
Conditional: If then
Truth value: False
Converse: If then
Truth value: True
For the False, notice that having , doesn't necessarily imply that , since would also render 36 when squared.
The answer is 7. Because $21.50-4=17.50 and then 17.50÷2.50=7