Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
Answer:
Step-by-step explanation:
In this problem, it is given that,
The stopping distance, D, in feet of a car is directly proportional to the square of it's speed, V.
We need to write the direct variation equation for the scenario above. It can be given by :
To remove the constant of proportionality, we put k.
k is any constant
Hence, this is the required solution.
Start by rearranging the question around where it’s y= so it would be y= 3x-9. Go down to -9 and place a point there, after go up three spots and move 1 point to the right. Keep doing that until you get your linear graph.
Hope that helped (:
Answer:
<em>Correct answer: C. (1,∞)</em>
Step-by-step explanation:
<u>First Derivative</u>
Given a real continuous function f(x), the first derivative f'(x) represents the slope of the tangent line for any value of x.
If the slope of the line is positive, then the function is increasing, if the slope of the line is negative, the function is decreasing.
The function to analyze is:
Computing the first derivative:
The function will be increasing when:
Dividing by 2:
Solving:
x > 1
This solution is represented by the interval (1,∞)
Correct answer: C. (1,∞)