A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Intern
et. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
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Cone details:
- height: h cm
- radius: r cm
Sphere details:
- radius: 10 cm
================
From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.
<u>Using Pythagoras Theorem</u>
(a)
TO² + TU² = OU²
(h-10)² + r² = 10² [insert values]
r² = 10² - (h-10)² [change sides]
r² = 100 - (h² -20h + 100) [expand]
r² = 100 - h² + 20h -100 [simplify]
r² = 20h - h² [shown]
r = √20h - h² ["r" in terms of "h"]
(b)
volume of cone = 1/3 * π * r² * h
===========================
To find maximum/minimum, we have to find first derivative.
(c)
<u>First derivative</u>
<u>apply chain rule</u>
<u>Equate the first derivative to zero, that is V'(x) = 0</u>
<u />
<u>maximum volume:</u> <u>when h = 40/3</u>
<u>minimum volume:</u> <u>when h = 0</u>
