Which fractions has the least common denominator of 24

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

qaws [65]

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.

6 0

3 years ago

Always, sometimes, or never.

irinina [24]

The ratio is always 1:1:√2

3 0

3 years ago

Nachelle goes out to lunch. The bill, before tax and tip, was $8.10. A sales tax of 4% was added on. Nachelle tipped 17% on the

harina [27]

Step-by-step explanation:

Nachelle goes out to lunch. The bill, before tax and tip, was $8.10. A sales tax of 4% was added on. Nachelle tipped 17% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.

6 0

2 years ago

Will someone help me

faust18 [17]

Answer:

1.one solution

2.no solution

3.ifinitly many

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Two beach rental companies compared their sales from last weekend. Both companies rent out jet skis and kayaks, and they charge

nignag [31]

Answer:

To rent a jet ski you need to pay $50 and to rent a kayak you need to pay $20

Step-by-step explanation:

Since both shops charge the same amount for each kind of vehicle, we will assign variables to the their cost. The cost of a jet ski will be "x" and the cost of the kayak will be "y". Therefore we can create a system of equations as shown below:

Will's shop:

12*x + 9*y = 780

Fun Rentals:

7*x + 11*y = 570

$\left \{ {{12x+ 9y=780} \atop {7x + 11y =570}} \right.\\$

We can isolate "x" on the second equation, we have:

$x = \frac{570 - 11y}{7}$

Applying this value on the first equation:

$12[\frac{570 - 11y}{7}] + 9y = 780\\\frac{6840 - 132y}{7} + 9y = 780\\\frac{6840 - 132y + 63y}{7} = 780\\ 6840 - 132y + 63y = 5460\\6840 - 69y = 5460\\69y = 1380\\y = 20$

Applying the value of "y" we found on the "x" equation above, we have: $x = \frac{570 - 11*20}{7}\\x = 50\\$

Therefore to rent a jet ski you need to pay $50 and to rent a kayak you need to pay $20

7 0

3 years ago

Which fractions has the least common denominator of 24 ​

Which fractions has the least common denominator of 24