14.81 radians/second
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
48 * 11 = 528
x=528
<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>
Answer:
47.8°
Step-by-step explanation:
Let's first outline the important parameters
--- <V = 90°
Vt = 64
UV = 43
The angles in a triangle sums up to 180,but we don't have up to 2 angles given so as to find the third one. What we have to is to find the second angle,in this case T,using the sine rule.
Sin v/v = sin t/t
(Sin 90)/64 = sin t/43
Cross multiply and we have
43 sin 90 = 64 sin t
Sin t = 43 sin 90 ÷ 64
Sin t = 0.6719
Sine inverse of t = 42.2°(the second angle)
Angle U = 180 -( 90 + 42.2)
180 - 132.2
= 47.8°
