<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>
Each hour,
x makes b/6 bearings
y makes b/4 bearings
z makes b/3 bearings
Together, each hour, x, y and z together make
b/6+b/4+b/3=b(1/6+1/4+1/3)=b(2/12+3/12+4/12)=b(3/4)=3b/4 bearings.
Time to make b bearings =
b/(3b/4)=4/3 hours = 1 hour 20 minutes.
Answer:
Absolutely anything! It all depends on what the equation is. Variables can be any number with exception of 0 As a denominator. Otherwise pick anything as long as the end results come out to the number you are seeking.
Answer:
-3/2
Step-by-step explanation:
Slope is defined as 
,
So the line goes down 6 instead of rising, making the rise negative: -6
The line goes over 4, making the run: 4
So -6/4 or -3/2
Answer:
₹ 4000
Step-by-step explanation:
Sarah's salary =₹ 30000
- one-tenth of her salary to an orphanage= 1/10*₹ 30000= ₹ 3000
- one-third of her salary is spent on food= 1/3*₹ 30000= ₹ 10000
- one-fourth of salary on rent and electricity =1/4*₹ 30000= ₹ 7500
- one-twentieth of her salary on the telephone= 1/12*₹ 30000= ₹ 2500
- donated some amount to the Prime Minister's relief fund = x
- She was left with ₹ 3000.
x= ₹ 30000- (₹ 3000+₹ 10000+₹ 7500+₹ 2500+₹ 3000)= ₹ 4000
