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indirectly proportional definition

From Wikipedia

Proportionality (mathematics)

In mathematics, two quantities are proportional if they vary in such a way that one of them is a constantmultiple of the other.

Symbol

The mathematical symbol 'âˆ�' is used to indicate that two values are proportional. For example, A âˆ� B.

In Unicode this is symbol U+221D.

Direct proportionality

Given two variables x and y, y is '(directly) proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that

y = kx.\,

The relation is often denoted

y \propto x

and the constant ratio

k = y/x\,

is called the proportionality constant or constant of proportionality.

Examples

• If an object travels at a constant speed, then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.
• The circumference of a circle is proportional to its diameter, with the constant of proportionality equal to Ï€.
• On a map drawn to scale, the distance between any two points on the map is proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.
• The force acting on a certain object due to gravity is proportional to the object's mass; the constant of proportionality between the mass and the force is known as gravitational acceleration.

Properties

Since

y = kx\,

is equivalent to

x = \left(\frac{1}{k}\right)y,

it follows that if y is proportional to x, with (nonzero) proportionality constant k, then x is also proportional to y with proportionality constant 1/k.

If y is proportional to x, then the graph of y as a function of x will be a straight line passing through the origin with the slope of the line equal to the constant of proportionality: it corresponds to linear growth.

Inverse proportionality

As noted in the definition above, two proportional variables are sometimes said to be directly proportional. This is done so as to contrast direct proportionality with inverse proportionality.

Two variables are inversely proportional (or varying inversely, or in inverse variation, or in inverse proportion or reciprocal proportion) if one of the variables is directly proportional with the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. It follows that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that

y = {k \over x}

The constant can be found by multiplying the original x variable and the original y variable.

Basically, the concept of inverse proportion means that as the absolute value or magnitude of one variable gets bigger, the absolute value or magnitude of another gets smaller, such that their product (the constant of proportionality) is always the same.

For example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.

The graph of two variables varying inversely on the Cartesian coordinate plane is a hyperbola. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since k can never equal zero, the graph will never cross either axis.

Hyperbolic coordinates

The concepts of direct and inverse proportion lead to the location of points in the Cartesian plane by hyperbolic coordinates; the two coordinates correspond to the constant of direct proportionality that locates a point on a ray and the constant of inverse proportionality that locates a point on a hyperbola.

Exponential and logarithmic proportionality

A variable y is exponentially proportional to a variable x, if y is directly proportional to the exponential function of x, that is if there exist non-zero constants k and a

y = k a^x.\,

Likewise, a variable y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x, that is if there exist non-zero constants k and a

y = k \log_a (x).\,

Experimental determination

To determine experimentally whether two physical quantities are directly proportional, one performs several measurements and plots the resulting data points in a Cartesian coordinate system. If the points lie on or close to a straight line that passes through the origin (0,&nbsp;0), then the two variables are probably proportional, with the proportionality constant given by the line's slope.

Unrelated proportionality

Given two variables x and y, y

Question:I'm doing past papers to try and get a little better at maths. I'm doing a direct proportion question, and I don't know when you divide two numbers, which one goes first. E.g: 90 = k x15 Then I've got 225 as being 15 , so, would I put "90 divided by 225" which gives me 0.4, or would I put "225 divided by 90" for 2.5? I think that the first number is what goes first in the division, but I'm not sure. D;

Question:Fully describe how you would set up a proportion to solve the following ? . In your description, think aloud and record your thoughts as you decide what is being compared and how you will set up each ratio. Be sure to include the definition of a proportion in your explanation. On a map, 1 cm represents 10 km. Wyoming is represented by a rectangle measuring 44.5 cm by 59.1 cm. Find the area of Wyoming im km^2. ( ^ = to the power of ) thank you so much!!!!

Answers:first find the area of wyoming on the map, to do this use A=lw A=(44.5cm)(59.1cm) A=2629.95cm^2 We know that 1cm=10km, square both sides to get 1cm^2=100km^2. Now we can set up a ratio... 1cm^2/100km^2=2629.95cm^2/Xkm^2 now solve for X X(cm^2)(km^2)=262,995(cm^2)(km^2) X=262,995 therefore the area of Wyoming in Km^2 is 262,995Km^2

Question:Hi. I just have a couple quick questions about indirect object prounouns (me, te, le). Please do NOT give me the definition of me, te and le since I already know what they mean. Here are my questions: 1) How do you know when to use the indirect object pronouns? For example, why do you use it in these sentences? "?Puedo pedirTE prestado tu casco?" "No puedo porque le prest mi bicicleta a Ramon." Also, could you please give a couple examples of when to use the indirect object pronouns and when not to use them? Thanks so much!