384π cm³ ( first one in list )
Calculate the volume (V) of the cone using the formula
V = 
πr²h ( r is the radius and h the height )
here r = 12 and h = 8
V = × 12² × 8 = 384π cm³ ← exact value
Answer:
$5
Step-by-step explanation:
Given data
We are given that
Large lemonade= $6
Small lemonade= $4
Total amount = 6+4= $10
He keeps 50% of the total
= 50/100*10
=0.5*10
= $5
Hence he will keep $5
Answer:
Step-by-step explanation: the x side is +5 and the y side is -15
There is a given point (10,3) this shows that when the width (X) is 10, the height (Y) is 3.
On the left side of the graph, they show an equation for the height Hw as being the constant over w ( width).
Using the given point solve for the constant.
Replace Hw with 3 and w with 10:
3 = Constant/10
Solve for the constant by multiplying both sides by 10:
Constant = 3 x 10
Constant = 30
The answer is B.
<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
