Activity 1: There is Math Around Us
Arithmetic sequence can be observed around us. Like the following fare rate
for first 4 kms of a modernized PUJ under General Community Quarantine
released by LTFRB last April 24, 2020.
Distance
Fare
First lailometer
11.00
Second kilometer
12.50
Third kilometer
14.00
Fourth kilometer
15.50
If we compute the increase of fare for every increase of kilometer distance,
they are all equivalent to 1.50. With this, the fare rate is an example of an
arithmetic sequence.
Aside from examples involving money, identify three situations or three
things that you see or observe in your surroundings that illustrate an
hmot
Answers
Answer:
i\red{Centroid(G)= \big(2,\frac{2}{3}\big)}Centroid(G)=(2,
3
2
)
\begin{gathered}\green{\begin{gathered}The\: coordinates \: of \\ the \: mid\:point \:of \: the \: sides \\of\:a\:triangle\:are\\ (1,1),(2,-3)\:and\:(3,4)\end{gathered}}\end{gathered}
Thecoordinatesof
themidpointofthesides
ofatriangleare
(1,1),(2,−3)and(3,4)
\begin{gathered}\orange{\begin{gathered}x_{1}=1,y_{1}=1;\\x_{2}=2,y_{2}=-3;\\x_{3}=3,y_{3}=4\end{gathered}}\end{gathered}
x
1
=1,y
1
=1;
x
2
=2,y
2
=−3;
x
3
=3,y
3
=4
\begin{gathered}\blue{\begin{gathered}Now,\\Centroid (G)=\big(\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3}\big)\end{gathered}}\end{gathered}
Now,
Centroid(G)=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)
\begin{gathered}\red{\begin{gathered}=\big(\frac{1+2+3}{3},\frac{1-3+4}{3}\big)\\=\big(\frac{6}{3},\frac{2}{3}\big)\\=\big(2,\frac{2}{3}\big)\end{gathered}}\end{gathered}
=(
3
1+2+3
,
3
1−3+4
)
=(
3
6
,
3
2
)
=(2,
3
2
)
Therefore,
\pink{Centroid(G)= \big(2,\frac{2}{3}\big)}Centroid(G)=(2,
3
2
)
Correct Question
The Correct question is below.
Concept
This question is activity-based and related to the arithmetic sequence which is the sequence where the common difference remains constant between any two successive terms.
Given
We have given the following fare rate for the first 4 km of a modernized PUJ under General Community Quarantine released by LTFRB last April 24, 2020. Distance Fare First kilometer 11.00 Second kilometer 12.50 Third kilometer 14.00 Fourth kilometer 15.50 If we compute the increase of fare for every increase of kilometer distance, they are all equivalent to 1.50. With this, the fare rate is an example of an arithmetic sequence.
To Find
We have to identify three situations or three things that we see or observe in our surroundings that illustrate an arithmetic sequence.
Solution
Here are three situations or three things that we see or observe in our surroundings that illustrate an arithmetic sequence:
(1) Let us consider a situation of seating around tables in a restaurant. A square table that fits only 4 people. When two square tables are put together, now 6 people can be seated. Put 3 square tables together and now 8 people are seated. This is the example of the arithmetic sequence where common differences remain constant i.e 2
(2) Let us consider another situation a writer writes 1000 words articles on the first day, 900 words on the second day, 800 words on the third day, and so on. This is the arithmetic sequence where common differences remain constant i.e 100 words.
(3) Let us consider the third situation that we are in a room where we are changing the temperature of the air conditioner (AC). Suppose it is at 25 degrees Celcius and feeling cold then increase it by 2 degrees, again feeling cold then again increasing it by 2 degrees, and so on. This is the arithmetic sequence where common differences remain constant i.e 2 degrees.
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