What is the area of her pasture if she decides to make two sides of 500 ft. Each and uses the angle you found in part (a)?

(a) The angle between them is 90 degrees

(b) The area is 125000ft^2

Step-by-step explanation:

Given

See attachment for complete question

Solving (a): Angle that gives the maximum area.

The area of a triangle is:

Where C is the angle between a and b.

The maximum area of a triangle is:

Equate both areas to find C

Divide both sides by

Take arc sin of both sides

The angle between them is 90 degrees

Solving (b): The area when

The area of a triangle:

So:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

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step-by-step explanation: