Answer:
<u>The sequence is</u>
- 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...
Each term is the sum of the consecutive numbers from 1 to that number.
<u>The nth term is the sum of the first n numbers:</u>
- aₙ = 1 + 2 + 3 + ... + n
- aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
- aₙ = n(n + 1)/2
1) The number of circles in the nth pile is n(n + 1)/2
2) When n tends to infinity the number of circles tends to infinity
Answer: As the dough rises, the distance between the raisins increases, indicating that the galaxies are moving apart.
Step-by-step explanation:
Answer:
29.42 units
Step-by-step explanation:
<u>1) Find the perimeter around the semi-circle</u>
To do this, we find the circumference of the circle using the given diameter:
where d is the diameter
Plug in 6 as the diameter
Divide the circumference by 2
Therefore, the perimeter around the semi-circle is 3π units.
<u>2) Find the perimeter around the rest of the shape</u>
Although it's impossible to determine the lengths of the varied sides on the right side of the shape, we know that all of those <em>vertical</em> sides facing the right add up to 6. We also know that all of those <em>horizontal </em>sides facing up add up to 7. Please refer to the attached images.
Therefore, we add the following:
7+6+7
= 20
Therefore, the perimeter around that area of the shape is 20 units.
<u>3) Add the perimeter around the semi-circle and the perimeter around the rest of the shape</u>
Therefore, the perimeter of the shape is approximately 29.42 units.
I hope this helps!
Answer:
The distance of the playground is 540m
Step-by-step explanation:
Here, we are interested in calculating the length of the playground given the information in the question.
Where to attack the question from is the segment that states that he took a break after 480m and also had 2 breaks. Thus, the distance traveled would be 480 * 2 = 960 m
Now, to find the length of the track, we add the distance covered plus the distance uncovered. Mathematically that would be 960m + 120m = 1,080m
In the last part of the question, we are told that the track is twice as long as the playground. This means that the length of the playground or the distance of the playground is 1080/2 = 540 m