The simple way of calculating a perimeter is to add all of the sides.
For a rectangle this would equal 2 x length + 2 x width
P = 2(6x + 3) + 2(-2x - 5)
= 12x + 6 - 4x - 10
= 8x - 4
At a higher level both the length and width must be greater than zero (= zero is a trivial rectangle)
6x + 3 > 0
6x > -3
x > -0.5
-2x - 5 > 0
2x + 5 < 0 (multiplying by -1 reverses the inequality)
2x < -5
x < -2.5
This rectangle cannot exist as x cannot be < -2.5 and > -0.5 at the same time!
-5/7 - (-6/7)z < -2/7
-5/7 + 6/7z < -2/7
6/7z = -2/7 + 5/7 = 3/7
z = 3/7 / 6/7 = 3/7 x 7/6 = 3/6 = 0.5
z = 0.5
The first answer to the first question is 27
the second answer to the second question is 2,875 million km
the third answer to the third question is <span>31680000</span>
Given:
Composite figure made of cylinder and two spheres.
To find:
The volume of the composite solid.
Solution:
Radius = 2 in
The value of π = 3.14
<u>Volume of sphere:</u>
Volume of a sphere is 33.49 in³
Volume of two spheres = 2 × 33.49 = 66.98 in³
Radius of cylinder = 2 in
Height of cylinder = 8 - 2 - 2 = 4 in
<u>Volume of cylinder:</u>
V = 3.14 × 2² × 4
V = 50.24
Volume of cylinder = 50.24 in³
Volume of composite solid = Volume of two spheres + Volume of cylinder
= 66.98 in³ + 50.24 in³
= 117.2 in³
The volume of the composite solid is 117.2 in³.
D shows equivalent expressions
