Answer:
17
Step-by-step explanation:
Answer:
A) 5/12
B) 5/12
C) 0/12
D) 11/12
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Q4.
A) 3/15
B) 4/15
C) 12/15
D) 8/15
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Q5.
A) 2/6 or 1/3
B) 4/6 or 2/3
C)
D)
Step-by-step explanation:
$65=$29+$9
- 29 -29
----------------
36 9x
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9 9
X=4
The example of exponential growth is: <span>c. y=0.5(1.5)x </span>
The function y = ab˟ is a can only be growth function if the value b>1. And if 0<b<1 it will decay. Therefore, the only correct value that fits the definition of exponential growth is option C.
<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>
