3. in a single growing season at the smith family orchard, the average yield per apple
tree is 150 apples when the number of trees per acre is 100. for each additional tree
over 100, the average yield per tree decreases by 1.
a. what would be the average yield per tree if the number of trees per acre was
doubled? what would be the total yield in that case?
b. how many trees should be planted per acre to maximize the total yield?

a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.

b. 25 more trees are to be planted per acre to maximize the total yield.

Step-by-step explanation:

If the no. of trees per acre is doubled then it will be equal to,

= 200

So, the no. of trees per acre is increased by (200 - 100) = 100

hence, the average yield per tree will be,

(150 - 100) = 50 in that case.

Hence, the total yield will be,

= 10,000 apples per acre

Now , if x trees are planted, the total no. of apples produced per acre will be,

=

= f(x) [say]

So. = f'(x)

= 50 - 2x---(1)

taking f'(x) = 0 , we get,

50 - 2x = 0

⇒ x = 25 --------------(2)

Again,

at x = 25

=  -2 (<0)

So, f(x) attains it's maximum value at x = 25

Hence,

25 more trees are to be planted per acre to maximize the total yield.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500