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3 years ago

Evaluate the function f(x) = 3x^-2x for x=4

Mathematics

1 answer:

liq [111]3 years ago

7 0

Answer:

3x^(-1)

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

3x(-2) • x

Step 2 :

Multiplying exponential expressions :

2.1 x(-2) multiplied by x1 = x((-2) + 1) = x(-1) = 1/x1 = 1/x

Final result :

3x(-1)

Processing ends successfully

plz mark me as brainliest :)

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3 years ago

Which one of the following fractions is the greatest? A. 1/2 B. 2/3 C. 3/4 D. 5/12

Maksim231197 [3]

Answer:

Step-by-step explanation:

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You have asked to design a rectangle box with a square base and an open top. The volume of the box must be620 cm to the 3rd powe

hammer [34]

Answer:

$69.21

Step-by-step explanation:

Since the box has a square base the length and breadth of the box will be equal. Let it be $x$

Let h be the height of the box

V = Volume of the box = $620\ \text{cm}^3$

$x^2h=620\\\Rightarrow h=\dfrac{620}{x^2}$

Now surface area of the box with an open top is given

$s=x^2+4xh\\\Rightarrow s=x^2+4x\dfrac{620}{x^2}\\\Rightarrow s=x^2+\dfrac{2480}{x}$

Differentiating with respect to x we get

$\dfrac{ds}{dx}=2x-\dfrac{2480}{x^2}$

Equating with zero

$0=2x-\dfrac{2480}{x^2}\\\Rightarrow 2x^3-2480=0\\\Rightarrow x^3=\dfrac{2480}{2}\\\Rightarrow x=(1240)^{\dfrac{1}{3}}\\\Rightarrow x=10.74$

Double derivative of the function

$\dfrac{d^2s}{ds^2}=2+\dfrac{4960}{x^3}=2+\dfrac{4960}{1240}\\\Rightarrow \dfrac{d^2s}{ds^2}=6>0$

So, x at 10.74 is the minimum value of the function.

$h=\dfrac{620}{x^2}\\\Rightarrow h=\dfrac{620}{10.74^2}\\\Rightarrow h=5.37$

So, minimum length and breadth of the box is 10.74 cm while the height of the box is 5.37 cm.

The total area of the sides is $4xh=4\times 10.74\times 5.37=230.7\ \text{cm}^2$

The area of the base is $x^2=10.74^2=115.35\ \text{cm}^2$

Cost of the base is $0.40 per square cm

Cost of the side is $0.10 per square cm

Minimum cost would be

$230.7\times 0.1+0.4\times 115.34=\$69.21$

The minimum cost of the box is 69.21 dollars.

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3 years ago

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