Answer: 334
Step-by-step explanation:
6 consecutive numbers can be written as:
n, n+1, n+2, n + 3, n + 4, n + 5,
The addition of those 6 numbers is:
n + n+1 + n+2 + n + 3 + n + 4 + n + 5
6n + 1 + 2 + 3 + 4 + 5 = 6n + 15
Let's find the maximum n possible:
6n + 15 = 2020
6n = 2020 - 15 = 2005
n = 2005/6 = 334.16
The fact that n is a rational number means that 2020 is can not be constructed by adding six consecutive numbers, but we know that with n = 334 we can find a number that is smaller than 2020, and with n = 335 we can found a number bigger than 2020.
So with n = 334 we can find one smaller.
6*334 + 15 = 2019
and we can do this for all the values of n between 1 and 334, this means that we have 334 numbers less than 2020 that can be written as a sum of six consecutive positive numbers.
Answer:
B. Scalene and D. Acute
Step-by-step explanation:
Check each answer.
A. Equilateral
All sides or all angles are not equal. So it is not equilateral.
B. Scalene
All sides are unequal. So it is scalene.
C. Obtuse
No any angle is greater than 90°. So it is not obtuse.
D. Acute.
All angles are less than 90°. So it is acute.
E. Isosceles
No two sides are equal. So it is not isosceles.
F. Right
No angle is 90°. So it is not right
Therefore, only answers B. Scalene and D. Acute are correct.
9514 1404 393
Answer:
d. 76(cos(3π/16) +i·sin(3π/16))
Step-by-step explanation:
To form the product of 38cis(π/8) and 2cis(π/16), multiply the magnitudes and add the angles:
38cis(π/8) × 2cis(π/16) = (38×2)cis(π/8 +π/16) = 76cis(3π/16)
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In this context, a·cis(b) ≡ a(cos(b) +i·sin(b))
