Hi can I get help with these two questions.
1. Everytime the pedals go through 360 degree rotation, the tires roate three imes. if the tires are 24 nches in diameter, what is the minimum numbe of comlete rotions of the pedls needed forr the bicycle to travel at least 1 mile.
I got 561 rotations.
2. If the sine of an angle is 3/5 and the ange is not in Quadrant I,what is the value of the cosine of the angle.
Is it -4/5 or -.79863551
1. each pedal moves the bike 3 pi* 2 ft = 18.85 feet. One mile is 5280 ft
5280 ft/18.89 ft/pedal = 280 rotations
I think you assumed the diameter was the radius.
2. If the sine is positive and the angle is not positve, you are in the second quadrant.
cosx = - sqrt (1 - sin^2x) = -4/5
Sure! I can help you with both of these questions. Let's break them down one by one.
1. To find the minimum number of complete pedal rotations needed for the bicycle to travel at least 1 mile, we need to calculate the distance covered by one complete pedal rotation and then use that information to determine the number of rotations needed for 1 mile.
First, let's calculate the distance covered by one complete pedal rotation. We are given that for every 360-degree rotation of the pedals, the tires rotate three times. Since the diameter of the tires is 24 inches, the circumference (distance around the tire) can be calculated using the formula: circumference = π * diameter.
So, the distance covered by one complete rotation of the tires is:
circumference = π * 24 inches = 75.3982 inches (approximately).
Next, we need to convert this distance to miles, since we want to know the number of pedal rotations needed for 1 mile. There are 12 inches in a foot and 5,280 feet in a mile. So, the conversion is:
distance in miles = distance in inches / (12 * 5280) miles.
distance in miles = 75.3982 / (12 * 5280) miles ≈ 0.00141939 miles.
Therefore, the distance covered by one complete pedal rotation is approximately 0.00141939 miles.
To find the minimum number of pedal rotations needed to travel at least 1 mile, we divide 1 mile by the distance covered by one complete pedal rotation:
Minimum number of pedal rotations = 1 mile / 0.00141939 miles ≈ 704.36 rotations.
Thus, the minimum number of complete pedal rotations needed for the bicycle to travel at least 1 mile is approximately 704.36 rotations. So it seems that your answer of 561 rotations is incorrect.
Now, let's move on to the second question.
2. We are given that the sine of an angle is 3/5, and the angle is not in Quadrant I. To find the value of the cosine of this angle, we need to use the relationship between sine and cosine. The Pythagorean identity states that sin^2(θ) + cos^2(θ) = 1.
Since we know the value of sine (3/5), we can use this information to find the cosine of the angle:
sin^2(θ) + cos^2(θ) = 1.
(3/5)^2 + cos^2(θ) = 1.
9/25 + cos^2(θ) = 1.
cos^2(θ) = 1 - 9/25.
cos^2(θ) = 25/25 - 9/25.
cos^2(θ) = 16/25.
Taking the square root of both sides, we get:
cos(θ) = ± √(16/25).
Since the angle is not in Quadrant I, the cosine value should be negative. Therefore, the value of the cosine is:
cos(θ) = -√(16/25) = -4/5.
So, the value of the cosine of the angle is -4/5.
I hope that helps! Let me know if you have any more questions.