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3 years ago

Find the circumference of the circle. Use 3.14 for pi

Mathematics

2 answers:

lapo4ka [179]3 years ago

8 0

Circumference = pi x diameter
pi = 3.14
diameter = 14 in

3.14 x 14 = 43.96 (option 1)

BabaBlast [244]3 years ago

3 0

Answer:

A. C = 43.96

Step-by-step explanation:

Circumference = Diameter * pi

Your diameter in this problem (given by the picture) = 14 inches.

If we plug this into the formula:

C = 14 * 3.14 = 43.96

There is a problem with your question, however, because the length we have found is in inches, while all of your options are in centimeters. However, converting the correct inches answers into centimeters is not an answer choice.

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2 years ago

If x^3 + 1/x^3 = 110 then find x + 1/x

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$Use:(a+b)^3=a^3+3a^2b+3ab^2+b^3\ (*)\\\\x^3+\left(\dfrac{1}{x}\right)^3\\=\underbrace{x^3+3\cdot x^2\cdot\dfrac{1}{x}+3\cdot x\cdot\left(\dfrac{1}{x}\right)^2+\left(\dfrac{1}{x}\right)^3}_{(*)}-3\cdot x^2\cdot\dfrac{1}{x}-3\cdot x\cdot\left(\dfrac{1}{x}\right)^2\\\\=\left(x+\dfrac{1}{x}\right)^3-3x-3\cdot\dfrac{1}{x}=\left(x+\dfrac{1}{x}\right)^3-3\left(x+\dfrac{1}{x}\right)$

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$x^3+\left(\dfrac{1}{x}\right)^3=110\iff \left(x+\dfrac{1}{x}\right)^3-3\left(x+\dfrac{1}{x}\right)=110\\\\subtitute\ t=x+\dfrac{1}{x}\\\\t^3-3t=110\ \ \ \ |subtract\ 110\ from\ both\ sides\\\\t^3-3t-110=0\\\\t^3-25t+22t-110=0\\\\t(t^2-25)+22(t-5)=0\ \ \ |use\ a^2-b^2=(a-b)(a+b)\\\\t(t-5)(t+5)+22(t-5)=0\\\\(t-5)[t(t+5)+22]=0\iff t-5=0\ or\ \underbrace{t^2+5t+22=0}_{no\ solution}\\\\t=5\iff x+\dfrac{1}{x}=5\\\\Answer:\boxed{x+\dfrac{1}{x}=5}$

3 0

3 years ago