Answer:
2
Step-by-step explanation:
what you do is -4(2)^-2 which is -1
then you do 3(5)^0 which is 3
then you add it together and it is 2
Answer:
see the explanation
Step-by-step explanation:
we know that
Every parallelogram can be made into a rectangle
so
With a parallelogram with a base of 6 and height of 2 you could create a rectangle with a base of 6 and height of 2
see the attached figure to better understand the problem
<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>
Substituting the values given, we get
(2)*(3) + 4 ;
Using BODMAS
We get
6 + 4
= 10
Answer:
628.32
Step-by-step explanation:
Volume:
πr2h
=π×52×8
= 200π
= 628.31853071796
