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Mathematics

1 answer:

vodka [1.7K]3 years ago

3 0

Since AB and BC are congruent, ABE is equivalent to CBE. ABE+CBE=ABC. So the answer would be 80 degrees.

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Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a ra

Dovator [93]

Circumference of a circle is C = 2πr.

part 1)

so the radius of the smaller gear is 3 inches, so after a full rotation, namely a revolution, the smaller gear has covered an arc of 2π(3), or 6π.

what angle has the larger gear of 7 inches in radius, has it covered with an arc of 6π?

$\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=6\pi \\
r=7
\end{cases}\implies 6\pi =7\theta \implies \cfrac{6\pi }{7}=\theta$

part 2)

since the larger gear has a radius of 7, in a revolution it will have an arc of 2π(7), or 14π.

now, we know the smaller gear does a 6π arc in a revolution, how many revolutions will it do in an arc of 14π?

$\bf \begin{array}{ccll}
arc&revolution\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
6\pi &1\\
14\pi &x
\end{array}\implies \cfrac{6\pi }{14\pi }=\cfrac{1}{x}\implies \cfrac{3}{7}=\cfrac{1}{x}\implies x=\cfrac{7}{3}$

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3 years ago

Fifty balls numbered 1 through 50 are mixed up in a barrel. How many balls must you draw from the barrel (without looking) to be

ipn [44]

If you draw only 25 balls, you could draw the 25 odd-numbered balls. However, there will then be no odd-numbered balls left, so when you draw two more you will be guaranteed to get two even-numbered balls. Thus, the minimum is 25+2=27 balls.

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3 years ago

Mark has a checking account. His opening balance on 1/7 was $110. The bank charges a 25¢ fee for each debit card transaction and

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110+30-(15+0.25)+40-(8+0.25)=156.5

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2 years ago

Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretchedit is 8 chi fr

drek231 [11]

Answer:

Height of the pole = 9.17 chi.

Length of the rope = 12.17 chi.