In-text Activities: Firm-Up/Deepen ActivitiesA relationship between two variables in such a way that one quantity increases or decreases the otherquantity also increases or decreases in a definite way is called a variation.Direct variation indicates that when..x (independent variable) increases, y (dependent variable) also increasesx (independent variable) decreases, y (dependent variable) also decreasesGraphically speaking, we can present direct variation14마(4 hrs, 120 milMathematically speaking, we can denote direct variation in the equation.y = kx where x is the independent variabley is the dependent variablek is the constant33 hrs, 90 miles)(2 hrs, 60 miles)2아(I hr, 30 miles)Verbally speaking, we can denote y = kx on the ff equivalent statements"y varies directly as x" "y varies as x""y varies with x""y is proportional to x'"y is directly proportional to x"As the number of hours increases, the distance increases.distance = dependenth varies directly as dhour - independenth = kdDirect power variation is a variation where one quantity varies directly as the power of the other quantity and presented asy- kx", k#0."y varies as the square of x""y varies directly as the square of x'Inverse variation indicates that whenGraphically speaking, we can present inversevariation in a graph way.x (independent variable) increases, y (dependent variable) decreasesx (independent variable) decreases, y (dependent variable) increasesMathematically speaking, we can denote inverse variation in the equation.y = or xy = k where x is the independent variabley is the dependent variablek is the constant1812length 97.2+2 3width4 5Verbally speaking, we can denote y = or xy =k on the ff. equivalentstatementsAs the width increases, the lengthdecreases."y varies inversely as x""y varies inversely with x""y is inversely proportional to x"width - independentlength = dependentL = +L varies inversely with w.Process questions:a. When can we say that the variation is:1. Direct variationAnswer2. Inverse variationAnswerb. Give at least 2 examples of real life situations:- Direct Variation3.4.Inverse Variation5.6.

The objective is to explain meaning of direct and indirect variation and give two examples of each.

Process questions: a. When can we say that the variation is: 1. Direct variation Answer 2. Inverse variation Answer b. Give at least 2 examples of real life situations: Direct Variation 3. 4. Inverse Variation 5. 6.

Process questions: a. When can we say that the variation is: 1. Direct variation Answer 2. Inverse variation Answer b. Give at least 2 examples of real life situations: Direct Variation 3. 4. Inverse Variation 5. 6.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

In-text Activities: Firm-Up/Deepen Activities
A relationship between two variables in such a way that one quantity increases or decreases the other
quantity also increases or decreases in a definite way is called a variation.
Direct variation indicates that when..
x (independent variable) increases, y (dependent variable) also increases
x (independent variable) decreases, y (dependent variable) also decreases
Graphically speaking, we can present direct variation
14마
(4 hrs, 120 mil
Mathematically speaking, we can denote direct variation in the equation.
y = kx where x is the independent variable
y is the dependent variable
k is the constant
3
3 hrs, 90 miles)
(2 hrs, 60 miles)
2아
(I hr, 30 miles)
Verbally speaking, we can denote y = kx on the ff equivalent statements
"y varies directly as x" "y varies as x"
"y varies with x"
"y is proportional to x'
"y is directly proportional to x"
As the number of hours increases, the distance increases.
distance = dependent
h varies directly as d
hour - independent
h = kd
Direct power variation is a variation where one quantity varies directly as the power of the other quantity and presented as
y- kx", k#0.
"y varies as the square of x"
"y varies directly as the square of x'
Inverse variation indicates that when
Graphically speaking, we can present inverse
variation in a graph way.
x (independent variable) increases, y (dependent variable) decreases
x (independent variable) decreases, y (dependent variable) increases
Mathematically speaking, we can denote inverse variation in the equation.
y = or xy = k where x is the independent variable
y is the dependent variable
k is the constant
18
12
length 9
7.2+
2 3
width
4 5
Verbally speaking, we can denote y = or xy =k on the ff. equivalent
statements
As the width increases, the length
decreases.
"y varies inversely as x"
"y varies inversely with x"
"y is inversely proportional to x"
width - independent
length = dependent
L = +
L varies inversely with w.
Process questions:
a. When can we say that the variation is:
1. Direct variation
Answer
2. Inverse variation
Answer
b. Give at least 2 examples of real life situations:
- Direct Variation
3.
4.
Inverse Variation
5.
6.

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