The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
Learn more about the recursive formula of sequence here:
brainly.com/question/14457800
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So we are trying to find this red line's length.
We can either find it directly, or use the blue line firs, and then use it as a leg for the green triangle.
So the blue leg is a hypotenuse for two of the edges. So:
from the Pythagorean Theorem
OR
Which works out to:
So now that we have that, using the Pythagorean Theorem again gives:
So the length of the red line is found that way.
But wait! There's more!
As it turns out, the red line can be found with an easier way that works with cubes and boxes (cuboids). It's really easy:
Where a, b, and c are all 10m, and d is the red line. This greatly reduces the math:
which gives the same answer as above, which you can see.
The ideal mechanical advantage of a slope is given by the ratio between the output load, which is simply the weight of the object (), and the input force applied to move the object along the slope:
The energy conservation law states that the potential energy of the object when it reaches the final height h is equal to the work done to move the object along the distance of the slope , i.e.
From this we find
Therefore, we can substitute this into the formula of the ideal mechanical advantage and calculate its value:
Please said thanks
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
5 days 6 hours 20 minutes
- 3 days 8 hours 40 minutes
============================
We will need to borrow minutes from the hours because we don't have enough.
1 hour = 60 minutes
6-1 = 5 hours
20 +60 = 80 minutes
5 days 5 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
We will need to borrow hours from the days because we don't have enough.
1 day = 24 hours
5 -1 =4 days
5 + 24 = 29 hours
4 days 29 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
1 day 21 hours 40 minutes