Answer:
) See annex
b) See annex
x = 0,5 ft
y = 2 ft and
V = 2 ft³
Step-by-step explanation: See annex
c) V = y*y*x
d-1) y = 3 - 2x
d-2) V = (3-2x)* ( 3-2x)* x ⇒ V = (3-2x)²*x
V(x) =( 9 + 4x² - 12x )*x ⇒ V(x) = 9x + 4x³ - 12x²
Taking derivatives
V¨(x) = 9 + 12x² - 24x
V¨(x) = 0 ⇒ 12x² -24x +9 = 0 ⇒ 4x² - 8x + 3 = 0
Solving for x (second degree equation)
x =[ -b ± √b²- 4ac ] / 2a
we get x₁ = 1,5 and x₂ = 0,5
We look at y = 3 - 2x and see that the value x₂ is the only valid root
then
x = 0,5 ft
y = 2 ft and
V = 0,5*2*2
V = 2 ft³
Answer:
16
Step-by-step explanation:
If 
, just put the number 
instead of 
.
So:
Answer:
3x + 2 ≤ 53
Step-by-step explanation:
"2 more than" means that there will be a + 2 in the equation. "3 times a number" means that 3 is multiplied by an unknown number which can be represented by a variable such as x. "At most" means less than or equal to, since the number cannot be greater than.
So generally, you might want to write the equation as 2 + 3x ≤ 53, but 2 + 3x is not in y = mx + b form. Basically, you need to write it as 3x + 2 ≤ 53 because that's how math works.
Multiply both sides by 2pi:
F(2pi) = sqrt(g/l)
Square both sides:
F^2 (2pi)^2 = g/l
Solve for l by dividing both sides by F^2 (2pi)^2
L = g/ F^2 (2pi)^2
Simplify:
L = g / 4pi^2(f^2)
