The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.
<h3>What is an inverse function?</h3>
A function that may convert into another function is known as an inverse function or anti-function.
If the function is f(x) = sinx + 2x + 1.
Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be
The derivative of f(x) will be
f'(x) = cos x + 2
Then the given value of a will be
a = 1
g(x) = f⁻¹(x)
put x = 0, then we have
f(0) = sin 0 + 2(0) + 1
f(0) = 1
Put x = 1, in the function f⁻¹(x). Then we have
f⁻¹(1) = 0
and
g(1) = 0
Then put a = 1, then we have
More about the inverse function link is given below.
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Cone details:
Sphere details:
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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
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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>
(792 bulbs) To answer this question one would multiply the number of rows times the number of bulbs 6 x132= ? to get the answer.
The easiest way to think of these is to put them in terms of percentages. Obviously, if you are SAVING 25%, you are SPENDING 75%. So if she SPENDS 13.50, we can easily use the 75% in an equation. $13.50 = .75x, with x being what the shoes cost originally. The .75 indicates that she is spending 75% of what the original cost is. You don't have any examples to pick from, but this is the best way to explain what one of the equations could be. You could also base it on money saved, but the equation is not quite as neat.
