Can you check the following, please?
1. Two minutes after a skydiver opens his parachute, he has descended 1900 feet. After 5 minutes, he descended 4750 feet. If distance varies directly with the time, at what rate is skydiver descending?
Ans: to find unit rate -1900/2 = 950
-4750/5 = -950
So, rate is -950 feet/minute.
2. Damon's earnings for four weeks from a part time job are shown in the table. Assume that his earnings vary directly with the number of hours worked. He can take a job that will pay him $7.35 per hour worked. Which job has the better pay?
Time worked: 15 12 22
Total Pay :112.50 90.00 165.00
Time worked: 9
Total Pay : 67.50
Ans: 112.50/15 = $7.50, 90/12 = $7.50, 67.50/9 = $7.50
So, current part job is better pay where $7.50 > $7.35.
3. A charter bus travels 210 miles in 3.5 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the bus will travel in 6 hours.
Ans: y = mx
210 = m(3.5)
210/3.5 = m
60 = m
y = 60*6hours
y = 360 miles in 6 hours
4. A monarch butterfly can fly 93 miles in 15 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the Monarch will travel in 24 hours.
Ans: y = mx
93 = 15m
93/15 = m
6.2 = m
y = 6.2(24hours)
y = 148.8 miles in 24 hours
#1, good
#2. yes
#3. yes
#4. yes
in #3, and #4 aren't you supposed to write the equation?
y = 3.5x , where x is in hours, and y is miles
and
d = 6.2t , where t is in hours and d in miles
1. The rate at which the skydiver is descending is -950 feet/minute.
2. The job that pays better is Damon's current part-time job, where he earns $7.50 per hour worked, which is higher than the $7.35 per hour offered by the other job.
3. The bus will travel 360 miles in 6 hours.
4. The Monarch butterfly will travel 148.8 miles in 24 hours.
Sure, let's go through each question and explain how to get the answers.
1. Two minutes after a skydiver opens his parachute, he has descended 1900 feet. After 5 minutes, he descended 4750 feet. If distance varies directly with the time, at what rate is the skydiver descending?
To find the rate at which the skydiver is descending, we need to find the unit rate of descent. Unit rate is calculated by dividing the change in distance by the change in time.
In this case, the change in distance is 1900 feet (from 0 to 1900) in 2 minutes and 4750 feet (from 0 to 4750) in 5 minutes.
So, the unit rate of descent is -1900/2 = -950 feet/minute and -4750/5 = -950 feet/minute.
Therefore, the rate at which the skydiver is descending is -950 feet/minute.
2. Damon's earnings for four weeks from a part-time job are shown in the table. Assume that his earnings vary directly with the number of hours worked. He can take a job that will pay him $7.35 per hour worked. Which job has the better pay?
To determine which job has better pay, we need to calculate the pay rate for each job. The pay rate is calculated by dividing the total pay by the number of hours worked.
For the first job, Damon earned $112.50 in 15 hours. So, the pay rate is 112.50/15 = $7.50 per hour.
For the second job, Damon earned $90 in 12 hours. So, the pay rate is 90/12 = $7.50 per hour.
For the third job, Damon earned $67.50 in 9 hours. So, the pay rate is 67.50/9 = $7.50 per hour.
Since the pay rate is the same for all three jobs and it's higher than the offered pay rate of $7.35 per hour, all three jobs have better pay.
3. A charter bus travels 210 miles in 3.5 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the bus will travel in 6 hours.
To find the distance the bus will travel in 6 hours, we can set up a direct variation equation based on the given information. In direct variation, the formula is y = kx, where y is the dependent variable (distance), x is the independent variable (time), and k is the constant of variation.
In this case, we know that the distance traveled is proportional to the time traveled, so we can write the equation as y = kx.
Using the given information, we have 210 miles = k * 3.5 hours. Solving for k, we divide both sides of the equation by 3.5: k = 210 / 3.5 = 60.
Now that we have the value of k, we can substitute it into the equation to find the distance traveled in 6 hours: y = 60 * 6 = 360 miles.
Therefore, the bus will travel 360 miles in 6 hours.
4. A monarch butterfly can fly 93 miles in 15 hours. Assume the distance traveled is directly proportional to the time traveled. Write and solve a direct variation equation to find how far the Monarch will travel in 24 hours.
Similar to the previous question, we can set up a direct variation equation to find the distance the monarch butterfly will travel in 24 hours.
The equation is y = kx, where y is the dependent variable (distance), x is the independent variable (time), and k is the constant of variation.
Using the given information, we have 93 miles = k * 15 hours. Solving for k, we divide both sides of the equation by 15: k = 93 / 15 = 6.2.
Now that we have the value of k, we can substitute it into the equation to find the distance traveled in 24 hours: y = 6.2 * 24 = 148.8 miles.
Therefore, the monarch butterfly will travel 148.8 miles in 24 hours.