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Mathematics

1 answer:

nalin [4]2 years ago

3 0

Answer:

c. 45d+.25m

Step-by-step explanation:

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Given the function f(x)=3x+5a / x^2-a^2 find the value of a for which f'(12) = 0

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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
 f(x)= ------------
 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
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Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)

Finally, a = -20 plus or minus 2sqrt(39)

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Rhombus has equal sides but its is different from a square because it looks like a diamond.
Rhombus also have parallel opposite sides and equal opposite angles.

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Help ..........................................