If I read the problem correctly, the cardboard is to be shaped into a box by cutting squares off of each corner and these turned up to make a box.
If this is the case, isn't the volume = x(22-2x)(16-2x) and the value of x to maximize the volume would be the derivative = 0?
If...

-6(4-3x)-5x = -24+18x-5x = 13x-24

1) First, look for greatest common factor.
Note: each term of x3 - 2x2 - 8x contains an x, therefore, this equals x(x2 - 2x - 8), found by dividing each term by x.
We now need to factor x2 - 2x - 8. What 2 factors of 8(1) subtract to equal 2? ...

I believe the hairs are searching for water.

It sounds like you need 3 combinations of 8 reds and 1 combination of 6 whites.
8C3 + 6C1 =8!/(3!5!) + 6!/(1!5!) = 56 + 6 = 62. Does this make sense?

OK. We need to find the volume of a cone and semicircle and add together.
Let Vs = volume of semicircle. Vs =½ (4/3)πr3 , and Vc = volume of a cone. Vc = (1/3)πr2h.
If r = 3.5 and h = 8.5, plug these values in and, voila, there is your...

Use the following identities: cot x = 1/tanx. and tan 2x = (2tanx)/(1-tan2x)
The equation then becomes (2tanx)/(1-tan2x) - 1/(tanx) = 0
Add 1/(tanx) to each side: (2tanx)/(1-tan2x) = 1/(tanx).
Multiply each side by tanx*(1-tan2x): 2tan2x...

If the problem is (x-2)2 = -8, then |x-2| = 2i√2, and x-2 = 2i√2 and x-2 = -2i√2.
So the answers are x = 2+2i√2, and x = 2-2i√2.

The Mean Value Thm states: If f(x) is continuous over [a, b], and f'(x) is defined over (a, b), where a<<b, then there is a c such that f'(c) = (f(b) - f(a))/(b - a). Try this and you should have your answer.
Therefore: f'(c) = -14c, and (f(5)-f(4))/(5-(-4))...

Hi, Carlos.
There are two ways to approach this problem. We need to put this equation into a different form.
f(x) = a(x-h)2 + k, so the vertex will be the point (h, k).
One way is to complete the square: f(x) = (x2 - 8x + ...

Remember, if this is an inequality, if you divide by a negative number, the inequality changes.
Therefore, -9x + 9 >= 4 x - 8 becomes -13x >= -17.
Divide by -13, and the answer becomes: x<= 17/13.

I don't see an equation. However, if your equation is in the form: 1x2 + bx = 0, in order to make sure the equation is a perfect square, divide b by 2, square it, and add to both sides.
Example: x2 + 6x = 0, b = 6, b/2 = 6/2 = 3, so (b/2)2...

How about the sum 2+3+4+...+(n+1) = 200?

a) The vertical asymptote is the value of x such that x-q = 0(i.e. when the f(x)-> ∞.
Therefore, x = q.
The horizontal asymptote is the value of f(x) when x-> ∞.
Therefore, y = 3 (the...

You can just divide the denominator into the numerator. eg. 3/4 = .75.

Again we have a perfect square.
Same process: y2 - 2/3y + 1/9 = 0 (How do we know that this is a perfect square? Take 1/2 of 2/3 = 1/3, square that and we get 1/9)
y2 - 2/3y + 1/9 = 0
(y -...

Note that the left side is a perfect square. If we rewrite the left side as a square, all that is needed to do is take the square root of each side.
x2 + 10x + 25 = 81
(x+5)2 = 81
√(x + 5)2 = √81
|x + 5| = 9
Therefore, ...

Another approach: 6x2 - 19x + 10
Try to find 2 numbers whose product is 60 (the product of the coefficient of x2 and 10, the constant), and whose
sum is 19. Try 15 and 4.
Rewrite to get 6x2 - 15x - 4x + 10
Factor by grouping: ...

Using the equation, y(t) = yoekt, where y(t) is the value of y at time t, yo is the value of y at time t = 0, and k is the rate at which y increases as a function of time.
Therefore, yo = 10,000 and k = .02.
a) y(0) = 10,000e0.02*0 = 10,000(1)...

a. R ∩ S = {3, 5}
b. R - T = {3, -2, 5, 7, 9}
c. ???