The functions f(x) = x2 – 3 and g(x) = –x2 + 2 are shown on the graph.
1 answer:
The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
<h3>How to modify the graphs</h3>The attached figure 1 represents the missing piece in the question
From the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
- Shift the function g(x) down by 2 units
- Reflect across the x-axis
- Shift the function g(x) down by 3 units
After the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Next, we plot the graph of the inequalities
From the graph of the inequalities, the curves of the inequalities have no point of intersection
Hence, the set of inequalities do not have a solution
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Answer:
The surface area of this cylinder is 3545 cm²
Step-by-step explanation:
The formula of the surface area of the cylinder is
- Surface area = later area + 2 base area, where
- Lateral area = perimeter of the base × height of the cylinder
Let us use the rules above to solve the question
∵ The base of the cylinder is a circle
∵ The perimeter of the circle = 2 π r
∵ The radius of the cylinder is 12 cm
∴ r = 12
∴ The perimeter of the base = 2 (12) (π)
∴ The perimeter of the base = 24π cm
∵ The height of the cylinder is 35 cm
∴ h = 35 cm
→ By using the rule of the lateral area above
∵ The lateral area = 24π × 35
∵ π =
∴ The lateral area = 24 × × 35
∴ The lateral area = 2640 cm²
∵ The area of the circle = π r²
∴ The area of the base = × (12)² =
(144) = 452
cm²
→ By using the rule of the surface area above
∴ The surface area = 2640 + 2(452) = 3545
cm²
∴ The surface area of this cylinder is 3545 cm²