Answer:
Last option; x < 2 and x > -1
Step-by-step explanation:
1. We know 2x − 1 < 3 and 2x − 1 > −3, so let's solve both of these inequalities.
2. (Solving for 1st condition)
Step 1: Add 1 to both sides.
Step 2: Divide both sides by 2.
3. (Solving for 2nd condition)
Step 1: Add 1 to both sides.
Step 2: Divide both sides by 2.
4. Now, we know that the value of x is greater than -1 but less than 2, and we can represent it on a number line like this:
Answer:
The volume of the composite figure is 84π ≅ 263.89 inches³
Step-by-step explanation
- The composite figure consists of :
# Half sphere with radius 3 inches
# Cylinder with radius 3 inches and height 6 inches
# Cone with radius 3 inches and height 4 inches
- The volume of the sphere is 4/3 π r³
∴ The volume of the half sphere = 1/2 × 4/3 π r³ = 2/3 π r³
- The volume of the cylinder is π r² h
- The volume of the cone is 1/3 π r² h
* Now lets solve the problem
- The volume of the half sphere
∵ The radius of the half sphere = 3 inches
∵ The volume of it = 2/3 π r³
∴ The volume = 2/3 × π × (3)³ = 18π inches³
- The volume of the cylinder
∵ The radius of the cylinder = 3 inches
∵ The height of the cylinder = 6 inches
∵ The volume of it = π r² h
∴ Its volume = π × (3)² × 6 = 54π inches³
- The volume of the cone
∵ The radius of the cone = 3 inches
∵ The height of the cone = 4 inches
∵ The volume of it = 1/3 π r² h
∴ Its volume = 1/3 π × (3)² × 4 = 12π inches³
- Add all the volumes to find the volume of the composite figure
∴ The volume = 18π + 54π + 12π = 84π = 263.89 inches³
* The volume of the composite figure is 84π ≅ 263.89 inches³
