Express using algebra.

Mathematics

2 answers:

Scorpion4ik [409]2 years ago

7 0

Answer:

1/3 of the original

Step-by-step explanation:

one piece is TWO times longer than the other one. if you break it in half you have three pieces that are all the same size

Fudgin [204]2 years ago

3 0

Answer:

The shorter piece is 4 in. long.

Step-by-step explanation:

The length of the shorter piece can be represented using x.

Thus, you can say that the longer piece is 2x (since it is twice as long as the other piece).

Since, the length of both the pieces will, for sure, add up to 1 ft, then we can say:

x + 2x = 1 ft

Which will simplify into:

3x = 1 ft (Divide both sides by 3)

x = 4 in. (Since 1 ft = 12 in., we can express it in different units unless you want a non-terminating decimal)

x = 4 in. is the length of the shorter piece since we established that x is the length of the shorter piece earlier on.

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Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a ra

pychu [463]

Draw a diagram to illustrate the problem as shown below.

When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.

Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°

Answer: 205.7° (nearest tenth)

Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions

Answer:
The smaller gear makes 1.75 rotations