Find the y intercept of a line with a slope of -4 and point (2,1)

A family wants to build a rectangular garden on one side of a barn. If 600 feet of fencing is available to use, then what is the

vovangra [49]

Answer: (A) $A=300l-l^{2}$

(B) Length varies between 1 and 150

(C) Largest area is 22500ft²

Step-by-step explanation: Suppose length is l and width is w.

The rectangular garden has perimeter of 600ft, which is mathematically represented as

$2l+2w=600$

Area of a rectangle is calculated as

$A=lw$

Now, we have a system of equations:

$2l+2w=600$

$A=lw$

Isolate w, so we have l:

$2w=600-2l$

w = 300 - l

Substitute in the area equation:

A = l(300 - l)

A = 300l - l²

(A) Function of area in terms of length is given by A = 300l - l²

(B) The practical domain for this function is values between 1 and 150.

(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:

A' = 300 - 2l

Find the values of l when A'=0:

300 - 2l = 0

2l = 300

l = 150

Replace l in the equation:

w = 300 - 150

w = 150

Now, calculate the largest area:

A = 150*150

A = 22500

The largest area the fence can enclose is 22500ft².

4 0

2 years ago

the circumference of the circle shown below is 54 centimeters. which expression gives the length in centimeters of XY?

g100num [7]

Answer:

The correct option is C

Step-by-step explanation:

Given the circumference of circle which is 54 cm and also the measure of arc XY is 120°

we have to find the expression for arc length of XY

The arc length can be calculated by the formula

$\frac{\theta}{360}\times 2\pi r$

$\frac{\theta}{360}\times circumference$

$\frac{120}{360}\times 54$

Hence, option C is correct

4 0

3 years ago

Read 2 more answers

What is one difference between fixed rate mortgages and variable rate mortgages

AURORKA [14]

The difference between a fixed rate and an adjustable rate mortgage is that, for fixed rates the interest rate is set when you take out the loan and will not change. With an adjustable rate mortgage, the interest rate may go up or down. Many ARMs will start at a lower interest rate than fixed rate mortgages.

4 0

3 years ago

What is the perimeter of the composite figure?

arsen [322]

Answer:

answer is 85 cm I hope it help

7 0

3 years ago

£2300 is invested in 4 years at 5% per year simple interest work out the total interest

Illusion [34]

Answer:

the answer i got was £46,000

Step-by-step explanation:

how i got this answer was that i multiplied £2300 • 5 and got £11,500 then i multiplied £11,500 • 4 and got £46,000

i hope this helps you.

7 0

3 years ago