Answer:
Correct option: Fourth one -> 2.2 cm
Step-by-step explanation:
The inside of the frame is 10 cm by 8 cm. To find the whole frame, we need to add two times the width of the metal to each dimension, so the final dimension is 10+2x cm by 8+2x cm.
The area of the frame itself is the area with the bigger dimensions (10+2x and 8+2x) minus the inside area (80 cm2)
If the final area is 100 cm2, we have that:
Area = (10+2x) * (8+2x) - 80
100 = 80 + 36x + 4x2 - 80
4x2 + 36x -100 = 0
x2 + 9x - 25 = 0
Using Bhaskara's formula to solve the quadratic function, we have:
Delta = 81 + 4*25 = 181
sqrt(Delta) = 13.45
x1 = (-9 + 13.45)/2 = 2.225 cm
x2 = (-9 - 13.45)/2 = -11.225 cm (not a valid measurement)
So the width x of the metal is 2.2 cm
Correct option: Fourth one
Use the midpoint formula it’s pretty straightforward from there. (-4.5 , -2)
Answer:
209.43951 round to the nearest tenth is 209.44
Step-by-step explanation:
A cone with a base radius of 5 units and a height of 8 units has a volume of 209.44 cubed units.
If a cone has a flat bottom, meaning the height and radius meet at right angles, then this formula can be used to find of volume ('V') of that cone (also know as a right circular cone):
V = 1/3(PI*r squared * h )
The volume of a cone can be calculated by taking one-third of the result of the radius squared, multiplied by the height, multiplied by the mathematical constant pi.
Here is a step-by-step case that illustrates how to find to volume of a cone with a radius of 2 feet and a height of 3 feet. Note that in order to save space (and because pi cannot be determine precisely) a limited number of decimal places are used, the symbol ~ denotes that this answer is an approximation.
V = 1/3(pi * r^2 * h)
= 1/3(pi * 2^2 * 3)
= 1/3(pi * 12)
= 1/3(37.7)
~ 12.6 cubic feet
Hope this helps!!