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3 years ago

The word "less than" represent what operation?

Mathematics

1 answer:

bixtya [17]3 years ago

4 0

Answer:

The term 'less than' is used to indicate the relationship between two values.

The term 'less than' symbolically represented as '<'.

Step-by-step explanation:

The term 'less than' is used to indicate the relationship between two values.

It expresses that one value will be lesser than the other.

The term 'less than' symbolically represented as '<'.

We can implement certain operations like comparing values, heights, and numbers.

For example, there are 3 pencils in one bag A, and 8 pencils in bag B.

When we compare the two, we can easily observe that bag A has fewer pencils than bag B.

Thus,

Pencils in Bag A < Pencils in Bag A

3 < 8

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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.