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scoray [572]
3 years ago
7

14. At what speed in miles per hour will a bicycle travel if the rider can cause the 26-inch diameter wheel to rotate 90 revolut

ions per minute? Round answer to the nearest tenth.
Mathematics
1 answer:
Gennadij [26K]3 years ago
8 0
So    a revolution is just another way to say 2π, so 96 revolutions will then be 96 * 2π, or 192π, so that means the angular speed = w 192 π/m

\bf v=rw\qquad 
\begin{cases}
w=\textit{angular speed}\\
r=radius\\
v=\textit{linear speed}\\
----------\\
w=\frac{192\pi }{m}\\\\
r=26
\end{cases}\implies v=\cfrac{\frac{192\pi }{m}}{26}
\\\\\\
v=\cfrac{4992\pi }{m} 


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Answer:

1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},

Step-by-step explanation:

1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}

2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}

3. This problem incorporates an exponent property.

Exponent property used: a^b\cdot a^c=a^{(b+c)}, yielding an answer of \boxed{5}

4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}

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3 years ago
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I need help with this math problem. I have to solve and show the the answer as well. I have to turn it in tomorrow.
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Since, 0.075 lieas between 0 and 0.5, therefore the event is said to be unlikely.

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2 years ago
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