A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the
circumference of the circular base of the cone and = 120°. Find:
a. the angle between [A F] and the base of the cone
a. the angle between [A F] and the base of the cone
1 answer:
Answer:
The angle between [A_F] and the base of the cone = 68.2°
The area of the base of the cone ≈ 12.57 m²
Step-by-step explanation:
The given parameters are;
The height of the cone = 5 m
The base radius of the cone = 2 m
The angle which the AC = 120°
Therefore, we have;
The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone
The angle between [CF] and the base of the cone = tan⁻¹(5/2) = tan⁻¹(2.5) ≈ 68.2°
∴ The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone = 68.2°
The angle between [A_F] and the base of the cone = 68.2°
The area of the base of the cone = π × r² = π × 2² = 4·π ≈ 12.57
The area of the base of the cone ≈ 12.57 m².
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Answer:
The correct option is (c) 13.277.
Step-by-step explanation:
The observed data is:
Location Observed sales (units)
Northside 70
Pleasant Township 75
Southwick 70
I-90 50
Venice Avenue 35
TOTAL 300
The test statistic for the Goodness of fit test is:
For <em>k</em> independent samples this test statistic follows a Chi-square distribution with degrees of freedom (<em>k</em> - 1).
The sample size in this case is, <em>k</em> = 5.
The degrees of freedom is, (<em>k</em> - 1) = 4.
The level of significance is, <em>α</em> = 0.01.
The critical value of the test is:
**Use the Chi-square table.
Thus, the critical value is 13.277.
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