Numbers prime to each other
Such numbers have only 1 as common factor even though they may be composite numbers e.g., 21 and 32 are prime to each other. We generally write (21, 32) = 1, which means 21 and 32 are prime to each other i.e., they have only one factor in common vi..
Example 3:
Factorise w 2 + 4w - 21..
Additive inverse of a Complex number
Let Z = a + i b and Z' = x + iy be the additive inverse of Z, then a + x = 0 and b + iy = 0 \ Additive inverse of a + ib is - a - ..
Let Z = a + i b and Z' = x + iy be the additive inverse of Z, then a + x = 0 and b + iy = 0 \ Additive inverse of a + ib is - a - ..Suggested answer:
Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the ..
Step 1: Factor pairs of the last term are (-7,+3), (21,-1), (+7,-3), (-21,+1). Step 2: The pair of factors whose sum is equal to the co-efficient of the middle term is (+7,-3). Step3: Rewrite the expression using these factors as w 2 + 7w - 3w -21. Step 4: Group the ..Suggested answer:
Let f(x) = 2x 3 + 4 a) When f (x) is divided by x-1, R = f (1) = 2(1) 3 + 4 = 6 b) When f (x) is divided by x-2, R = f (2) = 2(2) 3 + 4 = 20 d) When f(x) is divided by x+1, i.e., x-(-1). R = f(-1) = 2(-1) 3 + 4 = -2+4 ..
Let f(x) = 2x 3 + 4 a) When f (x) is divided by x-1, R = f (1) = 2(1) 3 + 4 = 6 b) When f (x) is divided by x-2, R = f (2) = 2(2) 3 + 4 = 20 d) When f(x) is divided by x+1, i.e., x-(-1). R = f(-1) = 2(-1) 3 + 4 = -2+4 ..Suggested answer:
HCF of 4,6,8 is 2. . HCF of b and is b. ..
HCF of 4,6,8 is 2. . HCF of b and is b. ..Question 10
Question: Four numbers are in AP. Sum of the first three is 21 and sum of last three is 30. Find the numbers. Answer: Let the numbers a - 3d, a - d, a + d, a + 3d be in AP. ..
Question: Four numbers are in AP. Sum of the first three is 21 and sum of last three is 30. Find the numbers. Answer: Let the numbers a - 3d, a - d, a + d, a + 3d be in AP. ..Verification by numerical problems
\ A + B = B + A \ A + B = B ..
\ A + B = B + A \ A + B = B ..Addition of Matrices
Addition of Matrices - To add two matrices: (i) Check whether they are of the same order. (ii) If they are of the same order, add the corresponding elements. (ii) It will be seen that the matrix obtained after addition will also be a matrix of the same order. If and then If and , th..
Addition of Matrices - To add two matrices: (i) Check whether they are of the same order. (ii) If they are of the same order, add the corresponding elements. (ii) It will be seen that the matrix obtained after addition will also be a matrix of the same order. If and then If and , th..Significant Figures and Measuring Instruments
Let us consider the following entries in a Students' Journal: (a) Weight of a calorimeter = 42 g (measuring instrument used is spring balance) The smallest reading the spring balance can record is 1g. There are 42 of 1 g units of measurement. Hence, there are two significant figures in the result. ..
Let us consider the following entries in a Students' Journal: (a) Weight of a calorimeter = 42 g (measuring instrument used is spring balance) The smallest reading the spring balance can record is 1g. There are 42 of 1 g units of measurement. Hence, there are two significant figures in the result. .. Result
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