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M

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

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

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Sachin replied | 27/11/2016

3abc.

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

Write the decimal expansion for: 63. 801?

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Shikha replied | 23/11/2016

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

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

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

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Sarvajeet replied | 26/11/2016

10+ 4x + (square of x).

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Sachin replied | 27/11/2016

sq of x + 4x+10

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A

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

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

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

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

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Factorization

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

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Ankit replied | 22/11/2016

2.

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D

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

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

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D

Dinnu replied | 03/12/2016

Not defined

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T

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

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

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Factorization

Simplify: a9 - 64a3 - a6 + 64?

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Factorization

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

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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 – 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 – 3(abc / a2b2c2)
= (1/a + 1/b + 1/c)3 – 3 / abc.
Thus, proved. «less

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

What do you mean by factorization?

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

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

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Sachin replied | 01/12/2016

No solution.

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

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

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Kamal replied | 19/11/2016

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

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Ram Mohan replied | 21/11/2016

The value of K = 15/4

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Answer

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P

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

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

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Priti replied | 19/11/2016

none because value of x or y is zero.

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

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

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Sachin replied | 01/12/2016

No. It is parallel to y-axis.

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J

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

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

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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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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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Answer

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S

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

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

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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.

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

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

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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  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

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?

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Chilla Rajesh replied | 30/11/2016

Father=14 and Child= 6.

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S

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

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?

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Digant replied | 24/11/2016

2.5 km/hr.

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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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Answer

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M

Martin 10/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

A motorboat can travel 30 km upstream and downstream 28 km in 7 hrs. It can travel 21 km upstream and return in 5 hrs. Find speed of the boat in still water and the speed of the stream?

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Saurabh replied | 04/12/2016

Let speed of boat is x km/hr: speed of stream is y km/hr
downstream = x+y upstream = x-y
therefore equation will be 30/x-y + 28/x+y =7
21/x-y + 21/x+y =5
let x-y= 1/p and x+y= 1/q
30p + 28q = 7 multiply 1 by 3 90p+84q=21
21p + 21q = 5 2 by 4 84p+84q=20...  more»
Let speed of boat is x km/hr: speed of stream is y km/hr
downstream = x+y upstream = x-y
therefore equation will be 30/x-y + 28/x+y =7
21/x-y + 21/x+y =5
let x-y= 1/p and x+y= 1/q
30p + 28q = 7 multiply 1 by 3 90p+84q=21
21p + 21q = 5 2 by 4 84p+84q=20

by solving we get p=1/6 q= 1/14 further x+y = 14 and x-y =6 x=10 and y=4 will be the answer. «less

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N

Naina 10/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

The angles of a triangle are x, y and 40 degree. The difference between the two angles x and y is 30 degree. Find x and y?

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Chandan replied | 22/11/2016

x+y+40=180 (Sum of all angle of a triangle is 180 degree)
hence x+y=140
x-y=30 (given)
adding both equations we get : 2x=170
hence x=85
putting x value in any equation we get y=55
hence x=85
y=55

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M

Mohan 10/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. What are the present ages, in years, of the son and the father?

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Shikha replied | 25/11/2016

Let son's age be x . Then father's age = 6x
4(x+4)=6x+4
4x+16-6x-4=0
-2x+12=0
x=-12/-2
=6
Son's age =6, father's ages is 36.

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A

Ashwini replied | 26/11/2016

Son age 8, fathers age 48.

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A

Ashish 10/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Linear Equations

A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number?

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Sreedevi replied | 07/12/2016

The number is 83.

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S

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

Solve the equation [(1 / 2) power 2x + 1] = 1?

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Sachin replied | 27/11/2016

-2x-1=0
-2x=1
x=-1/2

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