Angus Cut His Neighbors' Lawns For The Summer. By The End, He Had $325 In His Lawn-cutting Bank Account And He Paid A Total $75
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Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.
Above step we use "Multiplication property of equality"
In the above step we "Simplify on both sides of equation"
In the above step we use "Distribution property"
The above step is the result of using "Subtraction property of equality"
Above step is result of "Combining the like terms"
Above step is the result of using "Division property of equality"
Above step is result of "Simplifying fractions on either side of equation"
Let
x = wristbands
y = headbands
We then have the following inequations:
2x + 3y> = 50
x> = 5
The graph that represents the solution for this system of inequations is shown in the attached image.
The set of solutions is the shaded region.
x = wristbands
y = headbands
We then have the following inequations:
2x + 3y> = 50
x> = 5
The graph that represents the solution for this system of inequations is shown in the attached image.
The set of solutions is the shaded region.