Answer:
V=π(d
2)2h=π·(12.8
2)2·7.1≈913.62541ft³ Step-by-step explanation: because i said so
<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>
So there are two triangles here: Smaller one (ADE) and bigger one (ABC) and they both are similar.
So you can use proportions here.
AB / AC = AD / AE
AB = AD + DB = 6 + 1 = 7
AC = AE + 3
AD = 6
So plug in these values:
AB / AC = AD / AE becomes
7 / (AE + 3) = 6 / AE
Now do the cross multiply:
7 AE = 6 (AE + 3)
Now solve for AE:
7AE = 6AE + 18
AE = 18
If 3 ice cream cones cost 8.25 how much do 2 ice cream cones cost?
1 cone cost
8.25 : 3 = 2.75
2 cones cost
2.75 * 2 = 5.5
or
(8.25 : 3) * 2 = 5.5
Mode = 2
hope it helps
----------------------------
