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Graphical Method
While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependent variables are taken as ordinates. The points so plotted are joined by a smooth curve. For interpolation, the value of the independent variable is marked at the proper place on the X-axis and a line perpendicular to the X-axis is drawn from the point so marked to intersect the curve. Again by drawing a line perpendicular to the Y-axis from the point of intersection on the curve to meet the Y-axis, the value of the dependent variable is ascertained by reading off the value at the point of intersection with the Y-axis. The illustration given below demonstrates the use of this method.
Example
The population of a town is as follows:
Figure
Year
1941
1951
1961
1971
1981
1991
Population (in 000's)
24
30
40
54
78
104
Find the population for the years 1976 and 1978.
Marking points on the X-axis, for the years 1976 and 1978, and dropping perpendiculars, the population for the years can be interpolated as 65,000 and 70,000 respectively.
Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n ⇒ α = 14 ? n
what is the minimum money of an assignments?
Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n
27-81/3
1. (a) Give an example of a function, f(x), that has an inflection point at (1, 4). (b) Give an example of a function, g(x), that has a local maximum at ( -3, 3) and a local min
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
Give the Definition of Logarithms ? A logarithm to the base a of a number x is the power to which a is raised to get x. In equation format: If x = ay, then log a x = y.
calculate
The given figure consists of four small semicircles and two big semicircles. If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find
a local pizza store offers medium two-topping pizzas delivered for $6.00 per pizza plus a $1.50 delivery charge per order. on weekends, the store runs a game day special: if six or
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