If the sum of the first 20 square numbers is 2870 then sum of the first 21 square numbers is 3311.
Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The first square number is 1, and the sum of the first 20 square numbers is 2870.
We need to find the sum of the first 21 square numbers.
for first 20 numbers the answer is
n(n+1)(2n+1)/6
20*21*41/6 = 2870
Now we have to find the sum of first 21 square numbers.
21²=441
Now add it with 2870
2870+441=3311
Hence, the sum of the first 21 square numbers is 3311.
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Angles of a triangle always add up to 180 degrees. The given angles (90, 90, 20 degrees) give a total of 200 degrees, hence they cannot form a triangle.
In order for three angles to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the measures of any two angles in a triangle must be greater than the measure of the third angle.
In this case, you have angles measuring 90 degrees, 90 degrees, and 20 degrees. Let's apply the theorem:
1. Angle 1: 90 degrees
2. Angle 2: 90 degrees
3. Angle 3: 20 degrees
Now, let's check if these angles satisfy the triangle inequality theorem:
- Angle 1 + Angle 2 = 90 degrees + 90 degrees = 180 degrees
- Angle 3 = 20 degrees
According to the theorem, the sum of any two angles must be greater than the measure of the third angle. However, in this case, the sum of Angle 1 and Angle 2 (180 degrees) is not greater than Angle 3 (20 degrees). Therefore, these angles do not satisfy the triangle inequality theorem.
So, the answer is "no," 90 degrees, 90 degrees, and 20 degrees cannot form a triangle because they do not satisfy the triangle inequality theorem.
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Answer:
no. never.
Step-by-step explanation:
total internal angles of a triangle sum to 180. 90 + 90 is 180 so no, you cannot have a triangle with sides 90 90 and 20. it is possiblw to have 90 45 and 45 though