The answer: The absolute value
The function, as presented here, is ambiguous in terms of what's being deivded by what. For the sake of example, I will assume that you meant
3x+5a
<span> f(x)= ------------
</span> x^2-a^2
You are saying that the derivative of this function is 0 when x=12. Let's differentiate f(x) with respect to x and then let x = 12:
(x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
[x^2-a^2]^2
(144-a^2)(3) - (36+5a)(24)
------------------------------------ = 0
[ ]^2
Simplifying,
(144-a^2) - 8(36+5a) = 0
144 - a^2 - 288 - 40a = 0
This can be rewritten as a quadratic in standard form:
-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.
Solve for a by completing the square:
a^2 + 40a + 20^2 - 20^2 + 144 = 0
(a+20)^2 = 400 - 144 = 156
Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)
Finally, a = -20 plus or minus 2sqrt(39)
You must check both answers by subst. into the original equation. Only if the result(s) is(are) true is your solution (value of a) correct.
10.6470588 there ya go ;)
Answer:
1.00 inches
Step-by-step explanation:
The distance from vertex to focus is "p" in the quadratic equation ...
x^2 = 4py
In the given equation, p=1. Since units are inches, ...
the bulb should be placed 1.00 inches from the vertex.
First, lets observe this pattern.
We can notice that each number when multiplied by 3 gives the following number as:
4 x 3 = 12
12 x 3 = 36
36 x 3 = 108
108 x 3 = 324
Based on this, the next number in the pattern will be:
324 x 3 = 972
The right choice is:
c. 972
