CPhill

[ 14 * 9 ] - [ 12 * 8 ]  =

[ 126 ] - [ 96 ]  =

30 sq ft

Volume =  base area * height  / 3...so we have.....

24  = 9 * height / 3

24  =  3 * height       divide both sides by 3

8  =  height   [ in feet ]

f(x)=x^3−96x^2+400

The number of complex zeroes is either 2 or 0

Look at the graph :   https://www.desmos.com/calculator/eodpv407b2

There are 3 real roots....so.....no roots are complex

40 x 20 x 5  =  4000  cu ft 

Cube side length =

Cube root [ volume ]  =

Cube root [ 27 cubic yards ]  =

3 yards

A) altitude

Good job, AT

Here's the second one

y = -2x^2  + 32x - 12

The x coordinate of the vertex is    -32 / [ 2 ( -2 ) ]  =  -32 / -4  = 8

Since the first term is negative, this parabola turns downward, so we have a max at

-2 * 8^2  + 32 (8) - 12  =     -128 + 256 - 12 = 116

So...no y value can be > 116..so the range is   y ≤ 116 

Were you trying to solve an equation,OBT????

If so...post the problem and we'll see if we can solve it

Notice that 

-2 - √ 7  is an irrational number  [ can't be expressed as a fraction]

But    -4.646   is rational   [ can be expressed as a fraction ]

So......it's impossible to turn a rational into an irrational  -  and vice-versa......

13 x^2 -10x +350

When  x  =  8

13 * 8^2 - 10 * 8 +  350   =  1102