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ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories
Examples:
The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term.
Ans: a4= 0
⇒ a + 3d = 0
T.P a25= 3 (a11)
⇒ a + 24d = 3 (a + 10d)
⇒ a + 24d = 3a + 30d
RHS sub a = - 3d
- 3d + 24d = 21d
LHS 3a + 30d
- 9d + 30d = 21d
LHS = RHS Hence proved
Proof of the Properties of vector arithmetic Proof of a(v → + w → ) = av → + aw → We will begin with the two vectors, v → = (v 1 , v 2 ,..., v n )and w? = w
Question: The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tr
INTRODUCTION : When a child of seven isn't able to solve the sum 23+9, what could the reasons be? When she is asked to subtract 9 from 16, why does she write 9 - 16 = 13 ?
explain under a reflection the image is laterally inverted.
show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2
castor brought 6 3/4 carat cakes to share with 26 students. did castor bring enough for each student to have 1/4 of cake?
Average Function Value The average value of a function f(x) over the interval [a,b] is specified by, f avg = (1/b-a) a ∫ b f(x) dx Proof We know that the average
Conclude the values of the six trigonometric functions: Conclude the values of the six trigonometric functions of an angle formed through the x-axis and a line connecting the
supply chain management
when is the trnscribing process of data preparation irrelevant ? a)CAPI b) mall panel c) in home interview d) all of them
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