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lakkis [162]
3 years ago
12

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, th

en its volume is:
A) 36
B) 12sqrt3
C)18sqrt3
D)24sqrt3
E)36sqrt3

The correct answer was E. Hoping someone could explain how that is.
Mathematics
1 answer:
almond37 [142]3 years ago
5 0
Letter E is correct.
Area of equilateral trianlge= (1/2) tiime a^2 square root 3
Equation for the base is = x^2+y^2 =9

at x ,
y= square root (9-x^2)
Side of triangle a= 2y

d times Volume = (1/2)a^2 square root 3 dx

d times V= (square root 3) (9-x^2) dx

V= square root 3 INT (9-x^2) dx
-3V= 2square root INT (9-x^2) dx
0
V= 2 square root 3 ( 9x-x^3/3)

V=2 square root 3 ( 27-9)
V= 36 square root 3

The answer is E.
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Question 6 (1.25 points)
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Answer:

Test statistic Z= 1.713

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

A researcher wants to test if the mean annual salary of all lawyers in a city is

different from $110,000

Mean of the Population  μ = $110,000

Sample size 'n' = 53

Mean of the sample x⁻ = $114,000.

standard deviation of the Population = $17,000,

Level of significance = 0.01

Null hypothesis :

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

H₀:  x⁻ =  μ

Alternative Hypothesis :  x⁻ ≠  μ

<u><em>Step(ii)</em></u>:-

Test statistic

                 Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }

                 Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }

                Z =  1.7130

Tabulated value Z = 2.576 at 0.01 level of significance

The calculated Z- value =  1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the  mean annual salary of all lawyers in a city is  different from $110,000

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