The path of a ball is given by y=-1/20x^2+3x+5, where y is the height in feet and x is the horizontal distance in feet. find the maximum height of the ball and the horizontal distance at that height

The path of the ball is given by where y is the height in feet and x is the horizontal distance in feet.

We will use the second derivative test which states,

If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum. If, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum.

Firstly, we will calculate the first derivative of the given function,

To find the horizontal distance, let y'=0

Now let us consider the second derivative of the given function,

Since the second derivative that is y'' is negative.

Therefore, x=30 is the maximum horizontal distance.

Substituting x =30 in the given function to get the maximum height,

y=50 is the maximum height in feet.

answer: i think the answer is etheir c or d but i don't know which one but have a good day!

step-by-step explanation:

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.