1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tamiku [17]
3 years ago
9

A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the

garden, for each additional tree planted the yield will decrease by two apples per tree. (a) How many additional trees should be planted to maximize the total yield of apples
Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
5 0

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

Trees = 24

Yield = 104

x \to additional\ trees

So, we have:

Trees = 24 + x

Yield = 104 - 2x

Required

The additional trees to be planted for maximum yield

The function is:

f(x) = Trees * Yield

f(x) = (24 + x) * (104 - 2x)

Open bracket

f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x

f(x) = 2796 + 104x - 48x - 2x^2

f(x) = 2796 + 56x - 2x^2

Rewrite as:

f(x) = - 2x^2 + 56x + 2796

Differentiate

f'(x) = -4x + 56

Equate f'(x) = -4x + 56 to 0 and solve for x to get the maximum of x

-4x + 56 = 0

-4x =- 56

Divide by -4

x =14

The farmer should plant 14 additional trees, for maximum yield.

You might be interested in
Simplify the expression i⁸²
Elza [17]

Answer:

We can use a trick here. Let's look at the first few exponents of i to realize this:

i^0 = 1

i^1 = i

i^2= -1

i^3 = -i

i^4 = 1

i^5 = i

i^6 = -1

i^7 = -i

we can see that the pattern (1, i, -1, -i) repeats. Since 82/2 = 41, and 41 is only divisible by 1, i^41 = i, and i^2 = -1. -1*i = -i, so i^82 = -i.

Step-by-step explanation:

6 0
3 years ago
A family goes out to eat. The meal costs $44. The sales tax rate is 9%. They leave a 20% tip. How much did they spend?
REY [17]

Answer:

$56.76

Step-by-step explanation:

$56.76 because 20% of 44 is 8.80 which is the tip and 9% of 44 is 3.96 which is the tax rate giving you an answer of $56.76. Hope this helps!

6 0
3 years ago
Q6. The diagram shows two similar solids, A and B.
solniwko [45]

Answer:

640cm³

Step-by-step explanation:

Length SF = ×2

Volume SF = ×2³ = ×8

Volume of B = 8 × 80 = 640cm³

6 0
3 years ago
Find the value of (-17)-(40)+25
erica [24]

Answer:

-17-40+25

=25-57

= -32

4 0
3 years ago
What is the answer to 2-2×3+3
andreyandreev [35.5K]
2 - 2 x 3 + 3
= 2 - 6 + 3
= -4 + 3
= -1
7 0
3 years ago
Other questions:
  • What is the area of rhombus ABCD? Enter your answer in the box. Do not round at any steps. put the answer in units²
    5·1 answer
  • I NEED HELP FAST PLEASE!!!
    9·1 answer
  • - 2/3 ( 3 x -4 ) + 3x= 5/8<br> solve for x
    10·2 answers
  • I need the answer to this, i don’t understand this .
    7·1 answer
  • Question 40 and it about adding and subtracting polynomials
    14·1 answer
  • Plan g is paid 14,000 for a concert. If the money made is split at 2:5 between plan g and the arena. How much money did the aren
    11·1 answer
  • Help please tysm becuase this is hard
    13·1 answer
  • Please help me this is my final!!!
    9·2 answers
  • Find 7512−(−334) . Write your answer as a mixed number in simplest form.
    12·1 answer
  • Airplanes arrive at a regional airport approximately once every 15 minutes. If the probability of arrivals is exponentially dist
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!