9514 1404 393
Answer:
- domain: all real numbers
- range: y ≥ 0
Step-by-step explanation:
The function is defined for all values of x, so its domain is all real numbers.
The function can produce values of f(x) that are 0 or greater, so its range is ...
y ≥ 0
Answer:
the third answer
Step-by-step explanation:
c = 4
c + 1 = 1 + 1 + 1 + 1 + 1
4 + 1 = 1 + 1 + 1 + 1 + 1
5 = 5
<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>
The second question is number 3 for the polygon translation.
Question 3 is 2 units right and four units down.
Answer:
The value of x is -20/3.
Step-by-step explanation:
