1.you visit thr Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second,and so on in an arithmic sequence. What is the total distance the object will fall in 6 seconds?
2.After knee surgery, your trainer tells to return to your jogging slowly. he suggests jogging for 12 minutes each for the first week.Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are to jogging 60 minutes per day?
3.YOU complain that the hot tub in your hotel suite is not hot enough. The hotel tells you that they will increase the temperature by 10% each hour. If the current temperature of the hot tub is 75degree fa.What will the temperature of the hot tub after 3 hours, to the nearest tenth of a degree?
exquisite
1. d = 16*t^2.
1 s. 16 Ft.
2 s. 64 Ft.
3 s. 144 Ft.
d = 4.9*6^2 = 176.4 Ft in 6v s.
3. T = 75(1+0.10)^3 = 99.8o.
1. To find the total distance the object will fall in 6 seconds, we need to find the sum of the arithmetic sequence of distances fallen each second.
The first term (a) is 16 feet, and the common difference (d) is 32 feet (48 - 16 = 32).
We can use the formula for finding the sum of an arithmetic sequence:
Sn = (n/2)(2a + (n-1)d),
where Sn is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference.
Substituting the given values, we have:
Sn = (6/2)(2 * 16 + (6 - 1) * 32),
= 3(32 + 5 * 32),
= 3(32 + 160),
= 3(192),
= 576 feet.
Therefore, the total distance the object will fall in 6 seconds is 576 feet.
2. To find out how many weeks it will take for you to be jogging for 60 minutes per day, we need to set up an arithmetic sequence to represent the increasing jogging time each week.
The first term (a) is 12 minutes, and the common difference (d) is 6 minutes.
We want to find the number of weeks (n) that will make the jogging time 60 minutes.
Using the formula for finding the n-th term of an arithmetic sequence, we have:
an = a + (n-1)d,
Substituting the given values, we have:
60 = 12 + (n-1) * 6,
48 = 6(n-1),
8 = n-1,
n = 9.
Therefore, it will take 9 weeks for you to be jogging for 60 minutes per day.
3. To find the temperature of the hot tub after 3 hours, we need to calculate the temperature after each hour using the given temperature increase rate.
The temperature increase rate is 10% per hour.
We can calculate the temperature after each hour using the formula:
Tn = T0 * (1 + r)^n,
where Tn is the temperature after n hours, T0 is the initial temperature, r is the rate of increase, and n is the number of hours.
Substituting the given values, we have:
T3 = 75 * (1 + 0.1)^3,
= 75 * 1.1^3,
= 75 * 1.331,
= 99.825.
Therefore, the temperature of the hot tub after 3 hours will be approximately 99.8 degrees Fahrenheit.