You need the area of the sector created by the radii and the intercepted arc minus the area of the triangle created by the central angle of 120 and the segment BG. The area of the sector is, according to our info:
which is 10466.6666. Now we need the area of the triangle which is not as simple. If the central angle of the whole triangle is 120, then if we split it in half and deal with right triangles only, the angle measure is now 60, and we have a 30-60-90 special right triangle. If the hypotenuse (radius) is 100, in our pythagorean triple for that right triangle means that 100=2x and x = 50, which is going to be the side length for the side opposite the 30. That happens to be the height of the triangle, which we need for the area. We also need the base, which according to our Pythagorean triple, being the side across from the 60 degree angle, is 50 sqrt 3. but that's only half the side (we are still dealing with half of the whole triangle) and that means that the length of the whole side is 100 sqrt 3. Now we can find the area of the triangle:
which is
. Now subtract the area of the triangle from the area of the sector:
Answer:
1/64
Step-by-step explanation:
Notice that the common ratio is 1/4 since each term is being multiplied by 1/4 to get its successor's result.
Therefore, the 4th term would be 1 * 1/4 = 1/4, the 5th term would be 1/4 * 1/4 = 1/16, and the 6th term would be 1/16 * 1/4 = 1/64.
So, the 6th term of the geometric sequence is 1/64
Answer:
d=222
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>Errors in Algebraic Operations
</u>
It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them
- When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign
- When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive.
- Not to confuse product of fractions with the sum of fractions. Rules are quite different
The first expression is
Let's arrange into format:
We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is
Now for the second expression
Let's arrange into format
It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been
-4 straight down and 4 going to your right
