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allsm [11]
2 years ago
8

A=pir^2 solve for pi

Mathematics
1 answer:
VashaNatasha [74]2 years ago
6 0

Given problem;

   A = \pi r²

   Solve for π;

To solve for π implies that we make it the subject of the expression.

So;

       A = π r²

      Now multiply both sides by \frac{1}{r^{2} }

 So;

                A x \frac{1}{r^{2} }   = \pi x r² x \frac{1}{r^{2} }

              r² cancels out from the right side and leaves only π;

                  π = \frac{A}{r^{2} }

So    \pi  = \frac{A}{r^{2} }

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Answer:

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Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→1 3x x − 1
Reika [66]

Answer:

<h2>3/2</h2>

Step-by-step explanation:

Given the limit of a function expressed as \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx}), we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.

\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)

Since we got an indeterminate function, we will find the LCM of the function and solve again.

= \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= \lim_{x \to 1} \dfrac{3xlnx-3(x-1)}{(x-1)lnx}\\\\\\= \dfrac{3(1)ln(1)-3(1-1)}{(1-1)ln1}\\\\= \frac{3(0)-3(0)}{0(0)} \\\\= \frac{0}{0} (ind)

Applying L'hospital rule;

\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\=  \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)

Applying L'hospital rule again;

= \lim_{x \to 1} \dfrac{\frac{d}{dx} (3lnx)}{\frac{d}{dx} ((x-1)\frac{1}{x} +lnx)}\\\\=  \lim_{x \to 1} \dfrac{\frac{3}{x} }{(x-1)\frac{-1}{x^2} + \frac{1}{x} +\frac{1}{x} }\\\\= \dfrac{\frac{3}{1} }{(1-1)\frac{-1}{1^2} + \frac{1}{1} +\frac{1}{1} }\\\\= \frac{3}{0(-1)+2}\\ \\= \frac{3}{2-0}\\ \\= 3/2

<em>Hence the limit of the function is 3/2.</em>

7 0
3 years ago
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Answer:the qualirateral is in the wrong spot

Step-by-step explanation:

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