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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
write 107 in expanded form.
Q. How organize data by Circle Graphs? Ans. Circle graphs, or pie charts, are another way of organizing data sets into an easy-to-read format. They make it very easy to c
Applications of Integrals In this part we're going to come across at some of the applications of integration. It should be noted also that these kinds of applications are illu
Determine the derivative of the following function by using the definition of the derivative. f ( x ) = 2 x 2 -16x + 35 Solution Thus, all we actually have to do is to pl
25% of babies born at Yale New Haven Hospital weigh less than 6 pounds and 78% weigh less than 8.5 pounds. What percent of the babies born at Yale New Haven Hospital weigh among 6
Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
Determine an actual explicit solution to y′ = t/y; y(2) = -1. Solution : We already identify by the previous illustration that an implicit solution to this IVP is y 2 = t 2 -
2-3+=3+-4
If sin? = 1/2 , show that 3cos?-4cos 3 ? = 0. Ans: Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.
which ratio is largar. 1. 15:16 or 24:25
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