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Tamiku [17]
3 years ago
12

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

Mathematics
1 answer:
maria [59]3 years ago
6 0
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.
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Help plz???? I need help with math
tekilochka [14]

Surface area is the area of the faces added together.

First lets find the area of one of the triangles.

Area of triangle is 1/2*base*hight

Area=1/2*2*3= 3

Area of ONE tringle is 3, and area of the FOUR tringles is 4*3 whihc is 12

Now lets find area of square

area of square is side*side

So, area is 2*2 which is 4

Now lets add area of triangles+area of square

12+4 which 16

Surface area is 16

6 0
3 years ago
katy desea alquilar un barca y gastar por menos $54. El barco cuesta $7 por hora y katy tiene un cupom de descuento de $9 dolare
MAXImum [283]

Answer:

9 horas

Explanation:

$63 por 9 horas

Cupom de descuento de $9

$63 - $9 = $54

3 0
3 years ago
I really need the answer to this
bezimeni [28]

Answer:

$350

Step-by-step explanation:

9550-9200=350

7 0
3 years ago
Caylan is making bakes goose for a charity bake sale ha places a tray of scones a tray of muffing and a tray of cookies in the o
Varvara68 [4.7K]

Answer:

Step-by-step explanation:

an hour, or 60 minutes

3 0
3 years ago
Read 2 more answers
What is the cost of each item? What is the subtotal? What is the tax? What is the total paid? Shoes: $49.99 (normally) they are
prisoha [69]

Answer:

Cost of shoes = $37.4925

Cost of jacket = $92.4533

Tax = $9.81

Total paid = $144.2458

Step-by-step explanation:

Normal price of shoes = $49.99

Discount = 25%

Discounted price:

\$49.99 - \$49.99\times \dfrac{25}{100} = \$37.4925

Normal price of jacket = $137.99

Discount = 33%

Discounted price:

\$137.99 - \$137.99\times \dfrac{33}{100} = \$92.4533

Price of pack of cookies = $4.49

No discount on cookies as per question statement.

Total amount without tax = $37.4925 + $92.4533 + $4.49 = $134.4358

Sales Tax = 7.3% of total amount without tax = 7.3% \times $134.4358 = $9.81

Total paid = $134.4358 + $9.81 = <em>$144.2458</em>

4 0
3 years ago
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