18.

Mathematics

1 answer:

Katena32 [7]2 years ago

5 0

Answer:

$y = 10$

Step-by-step explanation:

$y= 2x + 1 \\ x = 5 \: \\ substitude \: 5 \: to \: the \: value \: of \: x \\ y = 5 \times 2 + 1 = 10 \\$

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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?

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

6 0

3 years ago

2 ÷ ___ = 4<br> A) 0.5 <br> B) 0.05 <br> C) 4 <br> D) 0.4

olga nikolaevna [1]

Heya!

2/0.5=4

You can check your work by multiplying 0.5*4.

3 0

2 years ago

76 divided into 6954

zhuklara [117]

91.5 I’m pretty sure

7 0

3 years ago