1. The average rate of change in a riders height between 1 and 3 seconds -30 ft/s
2. The average rate of change in a riders height between 0 and 5 seconds -24 ft/s
3. Another word for rate of change in this situation is speed
<h3>What is speed? </h3>
Speed is defined as the rate of change of the distance travelled with time. Mathematically, it can be expressed as:
Speed = distance / time
With the above idea, we can obtain the answers to the question given above.
<h3>1. How to determine the rate of change between 1 and 3 seconds</h3>
- Change in height = 30 - 90 = -60 ft
- Change in time = 3 - 1 = 2 s
- Rate of change =?
Rate = Change in height / change in time
Rate = -60 / 2
Rate = -30 ft/s
<h3>2. How to determine the rate of change between 0 and 5 seconds</h3>
- Change in height = 0 - 120 = -120 ft
- Change in time = 5 - 0 = 5 s
- Rate of change =?
Rate = Change in height / change in time
Rate = -120 / 5
Rate = -24 ft/s
<h3>3. what is another word for rate of change?</h3>
From the definition of speed given above, we can say that: another word for rate of change is speed
Learn more about speed:
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Try multiplying each side of the equation by 3, and then
watch out when the answer jumps off the paper at you.
<span>Using
the points (2, 45) (4, 143) and (10, 869), we can plug them into the
following system of 3 equations using the y = ax^2 + bx + c format:
45 = a(2)^2 + b(2) + c
143 = a(4)^2 + b(4) + c
869 = a(10)^2 + b(10) + c
which simplifies to:
45 = 4a + 2b + c
143 = 16a + 4b + c
869 = 100a + 10b + c
Solving the system, we get a = 9, b = -5, and c = 19. Thus the equation is:
c(x) = 9x^2 - 5x + 19
If you have a TI graphing calculator, you can also enter the points by
pressing Stat -> Edit and enter (2, 45) (4, 143) and (10, 869) into
it. Go back and calculate the QuadReg of the points from the Calc tab
and it will give you the same answer.
Now that we know the function that will produce the price of production
for any number of calculators, plug in x = 7 and it will give you the
price to produce 7 calculators.
c(x) = 9x^2 - 5x + 19
==> c(7) = 9(7)^2 - 5(7) + 19
==> c(7) = 441 - 35 + 19
==> c(7) = 425
Therefore, it costs $425 to produce 7 calculators.
Hope this helps.
</span>
Answer:
t=√d-12/4 and t=√-d-12/4, d≥12
Step-by-step explanation:
Hope this helps.
Here you have to find which each variable is, for this you start of picking one equation,
x + 2y + 6z = 4
-3x + 2y - 2 = -4
4x + 2z = 16
depending the equation you pick you multiply that by a certain number that will give you the opposite of one of the other equations,
-1(x + 2y + 6z = 4)
= -x -2y - 6z = -4
With this you add or subtract it with the equation that has the same number or variable, or both,
In this case it will be the equation,
-3x + 2y + 6z = 4
You can use this one or the third equation since both have a positive 2y which will cancel with -2y from the new equation,
-x - 2y - 6z = -4
-3x + 2y -z = -4
= -4x -7z = -8
Now you since you just eliminated the variable (y) you now have 2 variables, and the last equation has only 2 variables, meaning now you find the answer to those to equations,
-4x -7z = -8
4x + 2z = 16
= -5z = 8
Now leave the variable by itself,
z = 8/5
Now you found the variable (z), with this just substitute on one of the equations we used to find (z) so you can find (x), after that substitute those answered to on of the original equations so you can find (y)
