Graph the line y=-1/3x+2

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

3 0

Answer:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

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a rectangular field is 45 feet wide and is enclosed by 210 feet of fencing what is the area of the field in square feet

Helen [10]

Find the length of the field first. To do this, write a formula for the perimeter, P, of the field: P = 210 ft = 2(45 ft) + 2L.

Then 2L = 210 - 90 = 120, and L = 60 (feet).

The area of the field is thus WL = (45 ft)(60 ft) = 2700 sq ft

7 0

3 years ago

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.