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amid [387]
4 years ago
10

What is the smallest solution to the equation 2/3 x^2=24

Mathematics
1 answer:
True [87]4 years ago
7 0

Answer:

The smallest solution is -6

Step-by-step explanation:

2/3 x^2=24

Multiply by 3/2 on each side

3/2 *2/3 x^2=24 *3/2

x^2 = 36

Take the square root of each side

sqrt(x^2) = ±sqrt(36)

x = ±6

x = -6, 6

The smallest solution is -6

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Consider a wire of length 12 ft. The wire is to be cut into two pieces of length x and 12−x. Suppose the length x is used to for
Marat540 [252]

Answer:

x = 8

Step-by-step explanation:

When cutting the wire we will get two pieces

x             and          12 - x

If we build a circle whith x , the lenght of the circle will be x, and if we look at the equation for a lenght of a cicle  2*π*r = x

then r  = x/2π

and consequentely   A₁  = area of a circle  =  πr²       A₁  = π*x/2π  

A₁  = x/2

With the other piece  12  -  x     we have to make an square so wehave to divide that piece in four equal length

side of the square   =    s

s   = 1/4 ( 12 - x )    and the area is      A₂  = [1/4 ( 12 - x)]²

A₂  = ( 12 - x )²/16

Then     A₁  +  A₂  =  A(t)   and this area as fuction of x

A (x)  = x/2  +  1/16 ( 144 + x² -24x)          A (x)  =[ (8x + 144 + x² -24x)]/16

Taken derivatives in both sides

A´(x)  =  8  +  2x  - 24   = 0

   2x  -16  =  0         x  =  8    and   s =  12 - 8       s  =  4

7 0
4 years ago
<img src="https://tex.z-dn.net/?f=9%20-%204%20%5Csqrt%7B5%7D%20" id="TexFormula1" title="9 - 4 \sqrt{5} " alt="9 - 4 \sqrt{5} "
Korolek [52]

Answer:

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Step-by-step explanation:

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3 years ago
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3 years ago
What is g’(x)? Calculus derivative help
Dominik [7]

Answer:

12

Step-by-step explanation:

h'(x) = [f(x)*g(x)] '=f'(x )g(x) + f(x)g'(x)

h'(1) = [f(1)*g(1)] '=f '(1)g(1) + f(1)g'(1)

From the table f '(1)= -3,  g(1)=2,   f(1)= 3, g'(1) =6

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7 0
3 years ago
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