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tekilochka [14]

3 years ago

5

Jeanie wants to hang a circular mirror in a frame in her front wall. Determine the area of the largest mirror Jeanie can han if

the frame has a circumference of 56 inches.

1 answer:

AnnyKZ [126]3 years ago

3 0

56=2(pi)(r)
r=8.9127
pi(8.9127)^2=249.56cm^2
≈245cm^2 (3s.f.)

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Wewaii [24]

3.0? pretty sure that’s the answer

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3 years ago

Jonas went to the local barbershop for a haircut. The haircut cost $20. He gave the barber a 15% tip. What was the total cost, i

o-na [289]

Answer: 23 Dollars

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xxTIMURxx [149]

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3 years ago

Solve the answer y=6x−8<br> Thanks for helping

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3 years ago

Use logarithmic differentiation to find the derivative of the function. y = sqrt(x)e^x^2(x^2 + 5)^12

padilas [110]

$y=\sqrt x\,e^{x^2}(x^2+5)^{12}=x^{1/2}e^{x^2}(x^2+5)^{1/2}$

Take the logarithm of both sides and expand the right hand side:

$\ln y=\ln\left(x^{1/2}e^{x^2}(x^2+5)^{1/2}\right)$

$\ln y=\ln x^{1/2}+\ln e^{x^2}+\ln(x^2+5)^{12}$

$\ln y=\dfrac12\ln x+x^2\ln e+12\ln(x^2+5)$

$\ln y=\dfrac12\ln x+x^2+12\ln(x^2+5)$

Now take the derivative of both sides with respect to $x$ :

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}$

$\dfrac{\mathrm dy}{\mathrm dx}=\left(\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}\right)y$

$\dfrac{\mathrm dy}{\mathrm dx}=\left(\dfrac1{2x}+2x+\dfrac{24x}{x^2+5}\right)\sqrt x\,e^{x^2}(x^2+5)^{12}$

I'd stop there, but you could condense the right side a bit to get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x^4+21x^2+48x+5}{2x(x^2+5)}\sqrt x\,e^{x^2}(x^2+5)^{12}$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x^4+21x^2+48x+5}{2\sqrt x}e^{x^2}(x^2+5)^{11}$

8 0

4 years ago