Is N² + N always an even number? Explain
1 answer:
Answer:
Yes
Step-by-step explanation:
Yes.
Let's first start with even numbers. (N - even number)
Any even number squared, is an even number. Then, we add that squared even number to another even number which would give us an even number.
Now, let's see odd numbers.
Any odd number squared would be an odd number. When you add "N", it would be adding an odd number to an odd number, which gives you an even number.
OR
We can start by factoring the expression:
This is essentially multiplying two consecutive numbers, which in turn means that one number has to be even, and one has to be odd. An odd number multiplied by an even number will always be even.
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Answer:
1,809.98 lb*m/s^2
Step-by-step explanation:
First, we want to know how much weight of the boulder is projected along the path in which the boulder can move.
The weight of the boulder is:
W = 322lb*9.8 m/s^2 = (3,155.6 lb*m/s^2)
This weight has a direction that is vertical, pointing downwards.
Now, we know that the angle of the hill is 35°
The angle that makes the direction of the weight and this angle, is:
(90° - 35°)
(A rough sketch of this situation can be seen in the image below)
Then we need to project the weight over this direction, and that will be given by:
P = W*cos(90° - 35°) = (3,155.6 lb*m/s^2)*cos(55°) = 1,809.98 lb*m/s^2
This is the force that Samuel needs to exert on the boulder if he wants the boulder to not roll down.
we have
This is a mixed number
we know that
A mixed number is a combination of a whole number and a fraction.
So
is equal to
where
is the whole number
is the fraction
therefore
the answer is