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.
Answer:
x=3/2, 17√/2=3.56155281280883
Step-by-step explanation:
solve the equation (x2−3x−2)sin(x)=0 for x on the interval (−∞,∞)
- Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
- Factorize the equation by breaking down the middle term.
- Let’s identify two factors such that their sum is 7 and the product is -18.
Sum of two factors = 7 = 9 - 2
Product of these two factors = 9 × (-2) = 18
- Now, split the middle term.
- Take the common terms and simplify.
Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.
- Solving these two linear factors, we get
Answer:
it is 0
Step-by-step explanation: