Answer:
A separate answer sheet for Part I has been provided to you. Follow ... Record your answers to the Part I multiple-choice questions on the separate ... Your answer sheet cannot be accepted if you fail to sign this ... x V(x). 0. 4. 1 5.4. 2 7.29. 3 9.84. Which equation and statement ... Number of Candy Bars Sold.
Step-by-step explanation:
<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>
First of all you calculate the difference between the numbers:
10.5 - 10.653 = -0.153
10.5 - 10.592 = -0.092
10.5 - 10.732 = -0.232
10.5 - 10.484 = 0.016
You then select the difference with the smallest number (ignoring the positive and negative symbols). That happens to be the last one.
This means that the answer will be D) Spruce Trail.
Okay so 3x + 3 - 244 = -238 so I think you would put -238 on the number line and then fill in the line to the negative spot I hope that helps
Answer:
The length of each side is 26.3 cm
Step-by-step explanation:
Opposite sides of an isoceles triangle are equal
The isoceles triangle is divided into 2 right-angled triangles so the length of one side can be calculated using trigonometric ratio
When the isoceles triangle is divided, the angle in the right-angled triangle is 20° (1/2 of 40°) and the base is 9cm (1/2 of 18 cm), the hypotenuse side is calculated using trigonometric ratio
Let the length of the hypotenuse side be y
9/y = sin 20°
y = 9/0.3420 = 26.3
Length of each side is 26.3 cm
