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2 years ago

Rewrite, differentiate and simplify: 3/(2x)^3

Mathematics

1 answer:

Llana [10]2 years ago

8 0

$\frac{dy}{dx}$ = - $\frac{9}{8x^{4} }$

let y = $\frac{3}{(2x)^{3} }$ = $\frac{3}{8}$ $x^{-3}$

differentiate using the power rule

$\frac{d}{dx}$ ( $ax^{n}$ ) = na $x^{n-1}$

$\frac{dy}{dx}$ = - $\frac{9}{8}$ $x^{-4}$ = - $\frac{9}{8x^{4} }$

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Find the circumference of a circle whose area is 24

zalisa [80]

The answer is: " 17.35 " .

__________________________________

→ The circumference of the circle is: " 17.35 units " .

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The area, "A", of a circle:

A = $\pi$ * r² ;

Note: $\pi = 3.14$ .

The area of the circumference, "C", of a circle:

C = 2 $\pi$ r .

__________________________________________

Given:

A = 24 ;

Use the formula for the area, "A" of a circle, to find the radius, "r" .

Then, plug the value obtained for "r" into the formula for the circumference, "C" , of a circle:

C = 2 $\pi$ r l

To solve for the circumference, "C", of the circle.

________________

A = $\pi * r^{2}$ ;

24 = 3.14 * r² ;

↔ 3.14 * r² = 24 ;

Divide each side of the equation by "(3.14)" ;

[3.14 * r²] / 3.14 = (24) / (3.14) ;

to get:

→ r² = 7.64331210191 ;

Take the positive square root of each side of the equation;

to isolate "r" on one side of the equation; & to solve for the radius, "r" ;

→ ⁺√(r²) = ⁺√(7.64331210191) ;

to get:

→ r = 2.76281034802 ;

____________________________

Now, plug this "obtained value" for the radius, "r" into the equation for the formula for the circumference, "C" of a circle:

→ C = 2 $\pi$ * r ;

to solve for the circumference, "C", of the circle:

→ C = 2 * (3.14) * (2.76281034802) ;

= (6.28) * (2.76281034802) ;

= 17.3504489856 ;

→ round to: " 17.35 units" .

__________________________________

The answer is: " 17.35 " .

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→ The circumference of the circle is: " 17.35 units " .

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