Cone details:
Sphere details:
================
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>
<span>43.79 *0.05= </span>2.1895
218.95 *0.05= 10.9475
2.19 *0.05= 0.1095
21.90 *0.05= 1.095
2,189.50 *0.05= <span>109.475
</span>
hope this helps
-3n < 81...divide both sides by -3, change the inequality sign
n > -81/3
n > - 27 <==
** in an inequality, when dividing/multiplying by a negative number, the inequality sign changes
All squares are equal sides.Let X be the side of a square.Area of square,A = x^2
Here a tile is a square of side length 'x'. The following polynomial represents,
(x - 4) represents "the width of the new tile" (because 4 inches cut from the tile)
4x represents "the area removed from the tile" (since one side of removed tile is 'x' and other is 4 inches.)
x2 represents "area of original tile" of side equal to 'x'
x represents "the length of the new tile" (since length of new tile is not reduced. Length =x and breadth is x-4