The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have
The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have
The second sum is simply the sum of N ones:
So, the final result is
which ends the proof.
Answer:
Slope of parallel: -1/4
Slope of perpendicular: 4
y=mx+b
m=slope
parallel= slope
perpendicular= slope opposite
Answer:
1/2-7=1.5
Step-by-step explanation:
you're welcome
<span>1) force to pull it up 0.8 m
= 101.93 * 0.8
= 81.54 N
2) force for horizontal displacement
which can be found out by subtracting above value from total force applied
= 200-101.93
=98.07
Now finding horizontal displacement
98.07 = 101.93 * d
d= 0.96 m
Now since we found out hori. and vertical dist. apply Pythagoras theorem to find out length of ramp.
l^2= 0.96 ^2 + 0.8 ^2
= 0.9216 + 0.64
= 1.56
L = 1.25 m approx.</span>
