<u>Value of</u><u> </u><u>x</u><u> </u><u>is</u><u> </u><u>3</u><u>0</u><u>°</u>
Answer:
Solution given:
x°+(5x)°=180°[being straight line which sum of angle is 180°]
adding like terms
(6x)°=180°
dividing both side by 6
(6x)°/6=180°/6
x=30°
<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:1c . 3a . 4b . 5d . 2e
Step-by-step explanation:sorry if wrong not super good
It is D because if you look at the graph every 5 years the acres decrease by 20
Answer:
unlikely
Step-by-step explanation:
thats alot of people
