You have to make a cos graph that starts its minimum and of -2, has an amplitude of 10, a period of 10 and a maximum of 18.
I decided to use a cos graph since cos graphs start at their minimum or maximum unlike a sine graph that starts halfway between the minimum and maximum. You also know the amplitude has to be 10 since 18+2=20 and 20/2=10. We were also told that the water wheel completels a rotation every 10 minutes which means the period is 10 minutes.
lets start of with a regular cos(x) graph. This starts on its maximum instead of minimum so we have to multiply it by -1 to get -cos(x) which does start on its minimum.
-cos(x) has an amplitude of 1 instead of 10, to fix that we multiply it by 10 to get -10cos(x) which has an amplitude of 10.
-10cos(x) has a period of 2π instead of 10, to fix this we multiply the x by 2π/10 to get -10cos((π/5)x) which now has a period of 10.
-10cos((π/5)x) has a minimum of -10 and maximum of 10 instead of a minimum of -2 and maximum of 18, to fix this we add 8 to -10cos((π/5)x) to get -10cos((π/5)x)+8 which does have a minimum of -2 and maximum of 18.
Therefore the answer is y=-10cos((π/5)x)+8. x being time in minutes and and y being the height in feet.
I hope this helps. Let me know if anything is unclear.
So we are given a system:
Substitute x = 2 we get the system:
Multiply the first equation by -5 and the second by 2 we get the system:
Adding the two equations we get :
We find the value of y by using any of the other equations like this:
Final solution:
Answer:
<u>The track consumes ≅ 61 liters of fuel every 100 kilometres</u>
Step-by-step explanation:
As we can see in the graph, the total distance that the truck can travel with 500 liters of fuel is ≅ 825 kilometres.
For answering the question properly, we use the Rule of Three Simple, this way:
Kilometres Liters of fuel
825 500
100 x
Solving for x, we have:
825 * x = 500 * 100
825x = 50,000
x = 50,000/825
x = 60.6 liters of fuel (61 rounding to the next whole)
x ≅ 61 liters of fuel
<u>The track consumes ≅ 61 liters of fuel every 100 kilometres</u>
The new temperature is 60 degrees
