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
blagie [28]
3 years ago
9

A peach orchard owner wants to maximize the amount of peaches produced by her orchard.

Mathematics
1 answer:
qaws [65]3 years ago
6 0

Answer:

  a) Y(x) = {900, x≤30; 900-40(x-30), x>30}

  b) T(x) = {900x, x≤30; 2100x-40x², x>30}

  c) dT/dx = {900, x≤30; 2100-80x, x>30}

Step-by-step explanation:

a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

\displaystyle Y(x)=\left\{\begin{array}{lcl}900&\text{for}&x\le 30\\900-40(x-30)&\text{for}&x>30\end{array}\right.

__

b) The yield per acre is the product of the number of trees and the yield per tree:

  T(x) = x·Y(x)

\displaystyle T(x)=\left \{\begin{array}{lcl}900x&\text{for}&x\le 30\\2100x-40x^2& \text{for}&x>30\end{array}\right.

__

c) The derivative is ...

\displaystyle\frac{dT}{dx}=\left \{\begin{array}{lcl}900&\text{for}&x\le 30\\2100-80x& \text{for}&x>30\end{array}\right.

_____

The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.

You might be interested in
Write the prime factorization of 675 using exponent
matrenka [14]

675 : 5 = 135

135 : 5 = 27

27 : 3 = 9

9 : 3 = 3

3 : 3 = 1

675 = 5 · 5 · 3 · 3 · 3 = 5² · 3³

4 0
3 years ago
Write an algebraic expression that models each word phrase four more than a number b
Alisiya [41]
The answer would be the first choice 4+b
5 0
3 years ago
What is the Expanded Form for 27.39 using Powers Of 10's? Please help ASAP!!!
Licemer1 [7]
I think it's like 2.739 × 10
8 0
3 years ago
Givers the linear sequence,<br> -2,7,X,Y, 2... Find the value of<br> Z.
Harrizon [31]

Answer:

Z = 34

Step-by-step explanation:

From the series, we have that:

a = -2

a + d = 7

Hence, -2 + d = 7

∴ d = 7 + 2 = 9

a + 2d = X; a + 3d = Y and a + 4d = Z

-2 + 4(9) = Z

∴ Z = 36 - 2 = 34

7 0
3 years ago
The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334
kotykmax [81]

Answer:

282.7miles

Step-by-step explanation:

334+514=848inch

12inch=4miles

848inch=x

x =  \frac{818 \times 4}{12}  = 282.7

3 0
2 years ago
Read 2 more answers
Other questions:
  • Solve the equation 4 x/4 = 48 for x. Give the exact solution and an approximation to three decimal places.
    15·1 answer
  • Which is the closest approximation to the area of the circle?
    13·2 answers
  • Kaya used these steps to solve the equation 7+2x=2(x−1)+4. Which choice describes the meaning of her result, 7=2?
    15·1 answer
  • Х<br> 6 - 5 = (-13)<br> What does x equal?
    6·1 answer
  • PLEASE HELP I’m really confused about this
    5·2 answers
  • What is the value of the expression?
    8·2 answers
  • Which equation represents a line wit a slope of 5/2 and a y-intercept of -8/3?
    9·1 answer
  • Problem<br> Choose the inequality that represents the following graph. 32 points
    13·2 answers
  • in a bowl, there are green candies for every 5 red candies. If the bowl has a total of 160 candies (red and green only), which p
    8·2 answers
  • Solve number 11 pls
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!