Answer:
The domain for f(x) is all real numbers greater than or equal to 3.
Step-by-step explanation:
To solve the above equation, the value of x should be greater than or equal to 3, as we have the term and if value is less than 3, the term inside the square root will be negative and we cannot find the square root of negative numbers.
So, The domain for f(x) is all real numbers greater than or equal to 3.
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;
Part B:
When the small gear travels the same linear distance as the large gear in part A, we have;
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;
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
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
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