Answer:
Answer:
f(x) = - 4x + 4
Step-by-step explanation:
Step-by-step explanation:
A linear function has the form
f(x) = ax + b, thus
f(0) = a(0) + b = 4, that is
0 + b = 4 , hence b = 4
f(3) = 3a + b = - 8 ← substitute b = 4
3a + 4 = - 8 ( subtract 4 from both sides )
3a = - 12 ( divide both sides by 3 )
a = - 4, thus
f(x) = - 4x + 4
The answer is 7
because the equation is |(3)(-2)-1|
<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>
11,990
9% of 5500 is 495
(495+5500) [one year] x 2 [two years] = $11,990
At the end of 2 years, Aldo will owe $11,990.
45% of 450 is 202.50
$202.50 is the price of markup
$652.50 is the selling price
