2.2, 5/2, square root of 10, 7/2, -4.8
Answer:
x = 60
Step-by-step explanation:
By applying mean ratio theorem in the given right triangles ΔABC and ΔBDC,
BD² = AD × DC
BD² = 36 × 64
BD = 
BD = 48
By applying Pythagoras theorem in right triangle ΔADB,
AB² = AD² + BD²
x² = (48)² + (36)²
x² = 3600
x = 60
<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>
(7+11) is 18, (8/2) is 4, 18-4 is 14! If this expression is 6 less than her age, she would be 20!
