Answer:
Step-by-step explanation:
Find the sum of the first 42 terms of the following series, to the nearest integer.
2,7,12
Solution
The sum is given by
SUM_n=n/2*(a_1+a_n)
a_n=a_1+(n-1)d
a_1=2, n=42, d=5
The 42nd term is therefore given by
a_42=2+(42-1)5=207
SUM_42=42/2*(2+207)=21*209=4389
The sum of the first 42 terms of the series, therefore, is 4389
Answer:
if a·b=0, then either a=0 or b=0, or both
Step-by-step explanation:
just answered it on apex :)
The correct answer is 2.8 liters
Explanation:
The volume of the water in the bottle can be calculated by subtracting 3.5 liters from the volume of water the pail can hold (6.3 liters) because the volume in the bottle is 3.5 liters less than the one in the pail. Below, you can find the process.
volume in the pail - 3.5 liters = volume in the bottle
6.3 liters - 3.5 liters = 2.8 liters
This means the volume of water in the bottle is 2.8 liters. Also, you can double-check this answer by adding the volume in the bottle and the 3.5 liters (2.8 + 3.5 = 6.3).
When finding the reciprocal, it is basicaly flipping the numerator and denominator of the number. For instance, the reciporcal of 2 is 1/2, because the denominator of 2 would be 1. For an example more straight forward, the reciporacle of 3/5 is 5/3. This applied to the question goes as followed.
1. 3/5 is 5/3
2. 1/4 is 4
3. 1 is 1
Similarly when dividing fractions or an integer to a fraction, the fraction that is dividing the number turns into the reciprocal then you would multiply.
4. 3/(3/4) is 3*4/3= 4
5. 5/(3/4) is 5*(4/3)= 20/3
6. 8/(4/7) is 8*(7/3)= 56/3
7. 6/(3/5) is 6*(5/3)= 10
8. 2/(5/8) is 2*(8/5)= 16/5
9. 4/(8/9) is 4*(9/8)= 9/2
Using the cosine double angle formula,
(Note I took the positive case since 
terminates in the first quadrant)
Using the Pythagorean identity,
(Note I took the positive case since terminates in the first quadrant)
