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rjkz [21]
3 years ago
14

There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the numb

er of boys in the sixth grade is 5:7. Is Lonnie correct?
Mathematics
1 answer:
Keith_Richards [23]3 years ago
7 0
No, Lonnie is not correct because the correct answer is 5/6. If you do 35/42 divide both by 7, it'll be 5/6.
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The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease r
eduard

The large gear attached to the pedals connected to the smaller gear

attached to the wheel allows the bicycle to travel further per rotation.

Correct responses:

Part A: Approximately 10.47 inches

Part B: 300°The d

Part C: Approximately 125.66 inches

Part D: The distance traveled increases by approximately 62.83 inches

<h3 /><h3>Methods used to calculate the above values</h3>

Given:

The radius of the large central gear, <em>r</em> = 4 inches

Radius of the small gear = 2 inches

Part A:

The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;

\displaystyle Distance \ travelled \ by \ larger \ gear = \mathbf{\frac{150^{\circ}}{360^{\circ}} \times 2 \times \pi \times  4 \, inches} = \frac{10}{3} \cdot \pi \ inches

  • \displaystyle Distance \ traveled \ by \ the \ outer \ edge = \frac{10}{3} \cdot \pi \ inches  \approx \underline{ 10.47 \ inches}

Part B:

When the small gear travels the same linear distance as the large gear in part A, we have;

\displaystyle Degree \ of \ rotation = \frac{\frac{10}{3} \cdot \pi }{2 \times \pi \times  2 } \times 360^{\circ}= 300^{\circ}

  • The degree of rotation of the small gear = <u>300°</u>

Part C:

The distance travelled, <em>C</em>, by a single rotation of the large gear is given as follows;

C = 2 × π × 4 inches = 8·π inches

The degree of rotation of the smaller gear following one rotation of the large gear is therefore;

Degree  \ of \ rotation = \displaystyle \frac{8\cdot \pi \ inches}{4 \cdot \pi \ inches } \times 360^{\circ} = \mathbf{ 720^{\circ}}

720° = 2 × 360°

1 complete rotation is equivalent to 360°.

Therefore'

720° is equivalent to two complete rotation.

Therefore, the smaller gear and the wheel rotates twice for each rotation of the large gear

The distance the bicycle travels = 2 × The circumference of the wheel

Therefore;

Distance traveled by the bicycle = 2 × 2 × π × 10 inches = 40·π inches

  • Distance traveled by the bicycle = 40·π inches ≈ <u>125.66 inches</u>

Part D:

If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;

Number of rotation of the small gear for each rotation of the large gear = 3 rotations

Therefore, number of rotation of the wheel = 3

Distance the bicycle travels = 3 × 2 × π × 10 inches = 60·π inches

The difference in distance traveled = 60·π inches - 40·π inches = 20·π inches

  • The distance traveled by the bicycle increases by 20·π inches ≈ <u>62.83 inches</u>

Learn more about gear transmission here:

brainly.com/question/14646065

brainly.com/question/3926797

8 0
3 years ago
I need to find the standard form of this equation:<br> 4y^2+40y+3x+103=0
ExtremeBDS [4]
Hi!

The standard form would be

“4y^2+40y= -3x-103”


6 0
3 years ago
Ronnie can paint 8 rocks in 5 minutes. How long will it take him to paint 54 rocks
sergiy2304 [10]
8 rock in 5 minutes

54 rocks / 8 rocks = 6.75

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3 years ago
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An astronomy club wants to buy six new eyepieces for their telescope. Four of the lenses cost $53.98 each. Two lenses cost $21 e
Igoryamba
The answer is 257.92 dollars. Comment if you need more help :)
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FromTheMoon [43]

Answer:

oh god my calculator can't handle this

Step-by-step explanation:

so your answer is 3, take it or leave it

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3 years ago
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