Answeri dont know sorry
Step-by-step explanation:
The answer is 114sqrt{6} in³
A regular hexahedron is actually a cube.
Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²
Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²
D² = f² + a²
f² = 2a²
D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3
Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3
V = a³ = (D/√3)³
We have:
D = 8√2 in
Answer:
f(x) = -x³ + 3x² + 4x - 12
Step-by-step explanation:
f(x)=(x+2)(-x+3)(x-2)
Step 1. Use the difference of two squares
(x + 2)(x - 2) = x² - 4
f(x) = (-x + 3)(x² - 4)
Step 2. Long multiplication
x² - 4
<u>-x + 3 </u>
-x³ + 4x
<u> + 3x² - 12</u>
-x³ + 3x² + 4x - 12
f(x) = -x³ + 3x² + 4x - 12
Write a number as prime factors means to write the number as a product of numbers, all of which are prime. We start by checking whether the number is divisible by prime numbers, starting from the smallest prime number,2.
let's divide 24 into its factors.
first, it's even, so it must divide by 2
24=2*12
12 is also even, so it must divide by 2:
24=2*12=2*2*6
6 is also even, so it must divide by 2:
24=2*12=2*2*6=2*2*2*3
3 is not even, but it's a prime number.
so the solution is
2*2*2*3