You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of you
1 answer:
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Given:
Consider the below figure attached with this question.
∠EFH = (5x + 1)°, ∠HFG = 62°, and ∠EFG = (18x + 11)°
To find:
The measure of ∠EFH.
Solution:
From the figure it is clear that ∠EFG is divide in two parts ∠EFH and ∠HFG. So,
Isolate variable terms.
Divide both sides by 13.
The value of x is 4.
Therefore, the measure of ∠EFH is 21°.
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>
