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# Ask a Mathematics(Class IX-X Tuition) Question

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S

Sk 09/11/2016 in  Mathematics(Class IX-X Tuition),

If x + y + z = 0, show that: (cube of x) + (cube of y) + (cube of z) = 3xyz?

S

Saba replied | 05/12/2016

We know that, a 3 + b 3 + c 3 = (a + b + c)(a 2 + b 2 + c 2 - ab - bc - ca) + 3abc.
Substitute (a + b +c) = 0 in above equation:
=> a 3 + b 3 + c 3 = 0 x (a 2 + b 2 + c 2 - ab - bc - ca) + 3abc
=>a 3 + b 3 + c 3 = 3abc.

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N

Nagarunja 09/11/2016 in  Mathematics(Class IX-X Tuition),

Without actually calculating the cubes, find the value of: [cube of (-12)] + [cube of (7)] + [cube of (5)]?

Sachin replied | 27/11/2016

=3*-12*7*5
=-1260

Sreedevi replied | 02/12/2016

The given expression is in the form of (a+b+c)^3. As on adding a,b,c we are getting 0, we can apply the formula: If a+b+c = 0 then,
(a+b+c)^3 = 3 abc; On applying the above formula, we get (-12) ^3+(7)^3+(5)^3 = 3(-12)(7)(5) = - 1260.

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C

Chandramami 09/11/2016 in  Mathematics(Class IX-X Tuition),

If (square of x) + (inverse square of x) = 102, evaluate x + (inverse of x)?

Shambhavi replied | 07/12/2016

Squaring (x+1/x) , we get, (x^2+x^-2+2), but we know that x^2+x^-2 is equal to 102, thus (x+1/x)+2=102+2=104.

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M

Manmohan 09/11/2016 in  Mathematics(Class IX-X Tuition),

Evaluate: (a - 0.1) (a + 0.1)?

Neelabh Tiwari replied | 03/12/2016

Square of a - 0.01.

Chandan replied | 05/12/2016

We know that, ( (Square of a)- (Square of b)) = (a+b)(a-b).
Hence, (Square of a - 0.01) (Ans).

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S

Saravana 09/11/2016 in  Mathematics(Class IX-X Tuition),

Factorise: abx + aby - bcx - bcy?

Shambhavi replied | 07/12/2016

=(ab-bc)*x+(ab-bc)*y
=(ab-bc)(x+y)
Thus, factorized.

Barkha replied | 07/12/2016

[abx-bcx]+[aby-bcy]
taking x and y common terms
x(ab-bc) +y(ab-bc)
(ab-bc) is common term. So,
(ab-bc) (x+y)

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M

Madhusudhan 09/11/2016 in  Mathematics(Class IX-X Tuition),

If a + b + c = 0, then what is the value of [(cube of a) + (cube of b) +
(cube of c)?]

Sachin replied | 27/11/2016

3abc.

Chandan replied | 05/12/2016

[(cube of a) + (cube of b) + (cube of c)= 3 abc.
If a + b + c = 0.

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K

Krishna 09/11/2016 in  Mathematics(Class IX-X Tuition),

Write the decimal expansion for: 63. 801?

Shikha replied | 23/11/2016

6*10+3*1+8/1+0/10+1/100.

Mamata replied | 24/11/2016

6x(10^1)+3x(10^0) + 8 x (10^(-1)) +0x(10^(-2))+1x(10^(-3)).

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D

Divya 09/11/2016 in  Mathematics(Class IX-X Tuition),

Find the sum of: 5 + x - (square of x), 3x + 5 + 2(square of x)?

Sarvajeet replied | 26/11/2016

10+ 4x + (square of x).

Sachin replied | 27/11/2016

sq of x + 4x+10

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A

Ajit 09/11/2016 in  Mathematics(Class IX-X Tuition),

Subtract: 2(cube of x) - (square of x) + 4x - 6 from (cube of x) + 5(square of x) - 4x + 6?

Chandan replied | 22/11/2016

(cube of x) + 5(square of x) - 4x + 6-[ 2(cube of x) - (square of x) + 4x - 6 from (cube of x) ] = - (cube of x) + 6(square of x) - 8x + 12

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S

Sudha 09/11/2016 in  Mathematics(Class IX-X Tuition),

Multiply: (ax + by) (5x + 6y)?

Chandan replied | 22/11/2016

5a(square of x) + 6axy + 5bxy + 6b(square of y)

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T

Tanya 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

Find the value of x6 + 1 / x6, if x + 1 / x?

Ankit replied | 22/11/2016

2.

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D

Divya 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

If 4x - 4x - 1 = 24 then (2x)x equals what?

D

Dinnu replied | 03/12/2016

Not defined

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T

Thomas 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

Factorise: (cube of x) + x - 3 (square of x) - 3?

Shambhavi replied | 07/12/2016

x^3-3x^2+x-3 is the given equation. Taking x^2 as common from the first two terms, we get, x^2(x-3)+1(x-3) , which can be written as, (x^2+1)(x-3). Thus (x^2+1) and (x-3) are the factors of the equation.

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S

Sharath 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

Simplify: a9 - 64a3 - a6 + 64?

Shikha replied | 22/11/2016

Please see the attachment for full solution. Final factors are (a3-1) (a3-8) (a3+8).

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S

Shobhitha 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

Prove that: (1 / a3) + (1 / b3) + (1 / c3) = (1 / a + 1 / b + 1/c)3 + 3 / abc?

Shambhavi replied | 07/12/2016

we know that,
a3 + b3 + c3 = (a + b + c)3 -- 3(a + b)(b + c)(c + a)
a + b + c = 0 implies a + b = -- c, b + c = -- a, c + a = -- b.
(1/a)3 + (1/b)3 + (1/c)3
= (1/a + 1/b + 1/c)3 -- 3(1/a + 1/b)(1/b + 1/c)(1/c + 1/a)
= (1/a + 1/b + 1/c)3 -- 3(a+b / ab)(b + c / bc)(c + a / ac)
= (1/a + 1/b + 1/c)3 -- 3(-- c / ab)(-- a / bc)(-- b / ac)
= (1/a + 1/b + 1/c)3...  more»
we know that,
a3 + b3 + c3 = (a + b + c)3 â€“ 3(a + b)(b + c)(c + a)
a + b + c = 0 implies a + b = â€“ c, b + c = â€“ a, c + a = â€“ b.
(1/a)3 + (1/b)3 + (1/c)3
= (1/a + 1/b + 1/c)3 â€“ 3(1/a + 1/b)(1/b + 1/c)(1/c + 1/a)
= (1/a + 1/b + 1/c)3 â€“ 3(a+b / ab)(b + c / bc)(c + a / ac)
= (1/a + 1/b + 1/c)3 â€“ 3(â€“ c / ab)(â€“ a / bc)(â€“ b / ac)
= (1/a + 1/b + 1/c)3 â€“ 3(abc / a2b2c2)
= (1/a + 1/b + 1/c)3 â€“ 3 / abc.
Thus, proved. «less

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N

Neelima 09/11/2016 in  Mathematics(Class IX-X Tuition), Factorization

What do you mean by factorization?

Chandan replied | 22/11/2016

Factorisation:- The resolution of an entity into factors such that when multiplied together they give the original entity.

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K

Kripal 10/11/2016 in  Mathematics(Class IX-X Tuition),

What type of solution does the pair of equations have: x + 2y + 5 = 0, -3x - 6y + 1 = 0?

Sachin replied | 01/12/2016

No solution.

Sreedevi replied | 02/12/2016

On observing the given equations, we can say that the ratio of coefficients of 'x' and 'y' terms is same and is equal to (-1/3) but this is not equal to the ratio of constant terms. Hence, no solution.

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R

Renuka 10/11/2016 in  Mathematics(Class IX-X Tuition),

What is the value of k if the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel?

Kamal replied | 19/11/2016

If lines are parallel then 3/2=2 k/5

Ram Mohan replied | 21/11/2016

The value of K = 15/4

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P

Prabhash 10/11/2016 in  Mathematics(Class IX-X Tuition),

How many solutions does the pair of equation have: 2x + 4y = 3, 12y + 6x = 6?

P

Priti replied | 19/11/2016

none because value of x or y is zero.

V

Vimala replied | 19/11/2016

Consider 2/12 , 4/6 and 3/6
2/12 = 1/6
4/6 = 2 /3
3/6 = 1/2
Since all the above fractions are not equal, the solution of the above system is unique and hence the system is consistent.

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V

Vivek 10/11/2016 in  Mathematics(Class IX-X Tuition),

The line represented by x = 7 is parallel to the x - axis. Justify whether the statement is true or not?

Sachin replied | 01/12/2016

No. It is parallel to y-axis.

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J

Jaleeluddin 10/11/2016 in  Mathematics(Class IX-X Tuition),

For which value of k will the pair of equations: kx + 3y = k - 3, 12x + ky = k have no solution?

Ram Mohan replied | 21/11/2016

The given equations : k x+ 3 y=k - 3 ; and 12 x +k y=k will have no solution, if the ratios of coefficients of 'x' and that of 'y' are same. That is : if k/12 = 3/k, which implies k*k = 36==> k = - 6, or k = +6.
If K = -6, the two given equations modify into two parallel lines represented by, 2 x- y = 3 and 2 x- y = 1. which don't meet at all, and thus have no solution.
If...  more»
The given equations : k x+ 3 y=k - 3 ; and 12 x +k y=k will have no solution, if the ratios of coefficients of 'x' and that of 'y' are same. That is : if k/12 = 3/k, which implies k*k = 36==> k = - 6, or k = +6.
If K = -6, the two given equations modify into two parallel lines represented by, 2 x- y = 3 and 2 x- y = 1. which don't meet at all, and thus have no solution.
If k= -6, Both the equations, represent the same line 2 x + y = 1 in, which case too, there is no solution. «less

Ram Mohan replied | 21/11/2016

The given equations : k x+ 3 y=k - 3 ; and 12 x +k y=k will have no solution, if the ratios of coefficients of 'x' and that of 'y' are same. That is : if k/12 = 3/k, which implies k*k = 36==> k = - 6, or k = +6.
If K = -6, the two given equations modify into two parallel lines represented by, 2 x- y = 3 and 2 x- y = 1. which don't meet at all, and thus have no solution.
If...  more»
The given equations : k x+ 3 y=k - 3 ; and 12 x +k y=k will have no solution, if the ratios of coefficients of 'x' and that of 'y' are same. That is : if k/12 = 3/k, which implies k*k = 36==> k = - 6, or k = +6.
If K = -6, the two given equations modify into two parallel lines represented by, 2 x- y = 3 and 2 x- y = 1. which don't meet at all, and thus have no solution.
If k= 6, Both the equations, represent the same line 2 x + y = 1 in, which case too, there is no solution. «less

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S

Shyam 10/11/2016 in  Mathematics(Class IX-X Tuition),

Write a pair of linear equations which has the unique solution x = -1, y = 3. How many such pairs can you write?

Sreedevi replied | 07/12/2016

x+y=2 and x-y+4=0. The solution of pair of linear equations is (-1,3). We can write many equations like this.

Shambhavi replied | 07/12/2016

Formula to be used is:-
Present Value= Future Value/((1+r)^n), where r is discount rate and n in number of years.
So, Future value= 300 *((1+0.15)^10)+300 *((1+0.15)^9)+300 *((1+0.15)^8)+....+300 *((1+0.15)^1).

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D

Dhivya 10/11/2016 in  Mathematics(Class IX-X Tuition),

Solve: x + y = 3.3, 0.6 / (3x - 2y) = -1, 3x - 2y = 0?

Shambhavi replied | 07/12/2016

The second equation is undefined as denominator is 0, which is not possible. Thus these set of equations are inconsistent.

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A

Arvind 10/11/2016 in  Mathematics(Class IX-X Tuition),

Two years ago, salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Chilla Rajesh replied | 30/11/2016

Father=14 and Child= 6.

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S

Srinu 10/11/2016 in  Mathematics(Class IX-X Tuition),

A person, rowing at the rate of 5 km/hr in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream?

Digant replied | 24/11/2016

2.5 km/hr.

Tapas replied | 04/12/2016

Let the speed of the stream = v (in km/hr).
Total speed down the stream = (5+v) km/hr
Time to cover 40 km downstream, t1 = 40/(5+v)
Total speed up the stream = (5-v) km/hr
Time to cover 40 km upstream, t2 = 40/(5-v).
By the problem:-
t2 = 3 x t1
=> 40/(5-v) = 3 x 40/(5+v)
=> 5 + v = 3 (5 - v)
=> 4v = 10
=> v = 10/4 = 2.5 km/hr.

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