Suppose you work at a bowling alley. after work one day, you decide to line up bowling pins in a triangular
pattern with one pin in the first row, two pins in the second, three pins in the third, and so on.
(a)
how many total pins would you need to use in order to complete four rows?
(b) how many total pins would you need to use in order to complete ten rows?
(c) how many total pins would you need to use in order to complete one hundred rows?
how about one thousand rows?

The total pins to complete four rows is 10.

The total number of pins to complete 10 rows is 55.

The total number of pins to complete 100 rows is 5050.

The total number of pins to complete 1000 rows is 500500.

Explanation:

(a)

For fours rows, the arrangement will be like;

1 pin in one row, 2 pins in second row, 3 pins in third row and 4 pins in fourth row. Then total pins is,

Thus, the total pins to complete four rows is 10.

(b)

For 10 rows, apply the formula for sum of arithmetic progressions as,

Here, a is first term and d is common difference.

Thus, the total number of pins to complete 10 rows is 55.

(c)

For 100 rows, apply the formula as,

Thus, the total number of pins to complete 100 rows is 5050.

(d)

For 1000 rows, apply the formula as,

Thus, the total number of pins to complete 1000 rows is 500500.

For more details, refer to the link:

link

1) We are given that every row has one extra pin than the last one and since there are four rows and the First row start with 1 pin then the total number of pins in four rows would be- 1+2+3+4= 10

2) To complete 10 rows the total number of pins needed would be-  

Applying arithmetic progression to find out Sn = n/2 (2a + (n-1) d) = 5 x (2+9) =55

3) Now for 100 rows applying same formula again Sn = n/2 (2a + (n-1) d) = 50 x (2+99) =5050

4) Now for 1000 rows applying the formula Sn = n/2 (2a + (n-1) d) = 500x (2+999) =500500  

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.