Step-by-step explanation:
√-15 is a complex number which is written as √15¡
¡=√-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>
Answer: D. 94.25 in²
Step-by-step explanation:
To find the total area, we will break the shape up into two different parts.
[] The rounded part is 39.25 in². Let us assume the rounded part is exactly half of a circle.
Area of a circle:
A = πr²
Use 3.14 for pi:
A = (3.14)r²
Find the radius:
d / 2 = r, 10 / 2 = 5 in
Subsittue:
A = (3.14)(5)²
A = 78.5 in²
Divide by 2 since it is only half:
78.5 in² / 2 = 39.25 in²
[] The triangle is 55 in².
Area of a triangle:
A = b*h/2
A = 11 * 10 / 2
A = 110 / 2
A = 55 in²
[] Total area. We will add the two parts together.
55 in² + 39.25 in² = 94.25 in²
Answer:
7 books
Step-by-step explanation:
make an equation
x = # of books each book is $4 so its 4x
the shipping fee no matter how many books he buys will be $2 so it's just 2
the equation looks like this:
4x + 2 = 30
we set equal to 30 cuz he can't spend more than $30
solve for x
4x = 30 -2
4x = 28
x = 7
Brett can buy no more than 7 books.
