A rancher wants to fence in an area of 1500000 square feet inTO a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
x = width of rectangle
y = length of rectangle
A = area...

18=4+|2x|
14 = 2|x|
7 = |x|
x = ±7

a= 1 c=√11
If b is a leg, 1 + b^2 = 11
If b is the hypotenuse, b^2 = 1 + 11

Paula, did you leave out some parentheses?:
(c+8)/(c^2-5c+4) + (3c+5)/(c^2-9c+20) =
(c+8)/((c-1)(c-4)) + (3c+5)/((c-4)(c-5)) =
(c+8)(c-5)/((c-1)(c-4)(c-5)) + (3c+5)(c-1)/((c-1)(c-4)(c-5)) =
((c+8)(c-5)...

48000 = 9000(x)^9
x = (48/9)^(1/9) = (16/3)^(1/9) ≈ 1.204419106611659 is the growth factor.
r = x – 1 ≈ 0.204419106611659 ≈ 20.4419106611659% is growth rate

Let (x,y) be another point on the line.
Slope, m = (y - 3)/(x- -2) = (-6 - 3)/(1- -2) = -9/3 = -3
Multiply both sides by x+2:
y - 3 = -3(x+2) = -3x - 6
Add 3x + 3 to both sides:
3x + y = -3

16x^2 - 9y^2 - 32x - 54y - 209 = 0
16x^2 - 32x - 9y^2 - 54y - 209 = 0
16(x^2 - 2x) - 9(y^2 + 6y) - 209 = 0
16(x^2 + 2(–1)x + (–1)^2 – (–1)^2)
– 9(y^2 + 2(3)y + (3)^2 – (3)^2) - 209 = 0
16((x–1)^2 – 1) – 9((y+3)^2...

At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 60t +1060, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula
L(t) = 3t^2, where t is in minutes...

1. (√a+√b)/(√a–√b)
= (√a+√b)^2/((√a+√b)(√a–√b))
= (a + 2√(ab) + b)/(a–b)
2. Same technique as for 1.
3. 3√2 - 2√3
No simplification possible.
4. √3(√6 - 2√3)
= √3(√2 √3 - 2√3)
=...

√3h/2 ???
= √(3)*h/2, or √(3h)/2, or√(3h/2) ???
=====
4√x = 20
Divide both sides by 4:
√x = 5
Square both sides:
x = 25

Take two eggs.
Smash the blunt end of one on the counter.
Smash the sharp end of the other on the counter.
Which is stronger?
[Now scrape up the mess, pick out the shells, and make scrambled eggs.]

1. √(-25)√(-9) = (5i)(3i) = –15
2. (6i)^2 = (6i)(6i) = –36
3. 1/i = i/i^2 = –i
4. – √(3)√(-3) = – √(3) i√(3) = –3i
5. 1/(2–i) = (2+i)/((2+i)(2–i)) = (2+i)/5 = 2/5 + 1/5 i

f(x) = 64x^4 - 192x^3 + x^2 - 3x
f(x) = x(64x^3 - 192x^2 + x - 3)
f(x) = x( 64x^2(x - 3) + 1(x - 3) )
f(x) = x(x - 3)(64x^2 + 1)
f(x) = x(x - 3)((8x)^2 – (i^2))
f(x) = x(x - 3)(8x – i)(8x + i)

You measure angle of elevation from ground to top of building as 32°.
When you move 50 m closer to building, angle of elevation is 53°.
How high is building?
=====
h = height of building
x = distance from building when 53° elevation
tan(53°)...

For any point on the x-y plane, (x,y) = (r cos(θ), r sin(θ)), where the Initial Ray of θ is the positive x-axis and the Terminal Ray of θ starts at the origin and goes through (x,y).
r = √(x^2+y^2) is the distance from the origin to the point.
Then:
sin(θ)...

Please put parentheses around the exponent. Right now it looks like you have
(x^(-4) x + 8)/(5 x - 3)
= (x^(-3) + 8)/(5 x - 3)
= ((1/x)^3 + 2^3)/(5 x - 3)
=(1/x + 2)((1/x)^2 + 2/x + 4)/(5 x - 3)

Should this be sin(11 pi/12)?
11 pi/12 is in 4th quadrant where sine is negative.
sin(11 pi/6/2) = –√(( 1-cos(11 pi/6) )/2)
cos(11 pi/6) = cos(12 pi/6 - pi/6)
= cos(- pi/6) = cos(pi/6) = √(3)/2
sin(11 pi/6/2) = –√(( 1-√(3)/2...

"x in quadrant 2" means the terminal ray of the angle x is in quadrant 2.
If a and b are positive numbers, then (-a,b) is a point in quadrant 2.
We know any point can also be represented as (r cos(x), r sin(x) ), so:
(r cos(x), r sin(x) ) =...

Carefully graph the points and you will see they seem to lie on a straight line.
To prove it, find slopes between adjacent points in the list; if they all are the same, then it's a line.
(3,11)
(-1,3): (11-3)/(3- -1)=8/4=2
(5,15): (15-3)/(5- -1)=12/6=2
(-4,-3):...

A farmer is planning to put in a garden next to his barn. He is planning to fence in the garden on three sides (the barn will make the fourth side). He has 100 feet of fencing to use. FIND AN EQUATION FOR THE AREA OF THE GARDEN. Explain/Show work.
x = width of garden
y = length...