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Posted by Prince Raj 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Let the speed of the passenger train be x km/hr. Then, the speed of express train will be (x + 11)km/hr
Time taken by the express train to cover 132 km {tex} = \frac{{132}}{x+11}hrs{/tex}
Time taken by the passenger train to cover 132 km {tex} = \frac{{132}}{x }hrs{/tex}
According to the question ;
{tex}\therefore \frac{{132}}{{x }} - \frac{{132}}{x+11} = 1{/tex}
{tex}\Rightarrow \frac{{132(x+11) - 132x }}{{x(x +11)}} = 1{/tex}
{tex}\Rightarrow{/tex} 132x - 132x + 1452 = x(x +11)
{tex}\Rightarrow{/tex} 1452 = x2 + 11x
{tex}\Rightarrow{/tex} x2 + 11x - 1452 = 0 , This is the required quadratic equation.
Posted by Priya Singh 6 years, 9 months ago
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Posted by Kala Devi 6 years, 9 months ago
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Anam Khan 6 years, 9 months ago
Posted by 𝖄𝓸𝓰𝓲𝓽𝓪♛🖤😎 𝒴𝒶𝒹𝓊𝓋𝒶𝓃𝓈𝒽𝒾🔥🔥 6 years, 9 months ago
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Yogita Ingle 6 years, 9 months ago
let us assume that √7 be rational.
then it must in the form of p / q [q ≠ 0] [p and q are co-prime]
√7 = p / q
=> √7 x q = p
squaring on both sides
=> 7q2= p2 ------ (1)
p2 is divisible by 7
p is divisible by 7
p = 7c [c is a positive integer] [squaring on both sides ]
p2 = 49 c2 --------- (2)
Subsitute p2 in equ (1) we get
7q2 = 49 c2
q2 = 7c2
=> q is divisible by 7
thus q and p have a common factor 7.
there is a contradiction
as our assumsion p & q are co prime but it has a common factor.
So that √7 is an irrational.
Posted by Shikha Singh 6 years, 9 months ago
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Yogita Ingle 6 years, 9 months ago
867 is grater then 225
867=225×3+192
225=192×1+33
192=33×5+27
33=27×1+6
27=6×4+3
6=3×2+0
Therefore HCF of 867 and 225 = 3
Anjali Sontakke 6 years, 9 months ago
Posted by Mr.Poet ? _Prankster?_ Error 444? 6 years, 9 months ago
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Posted by ????? ?????? 6 years, 9 months ago
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Shreyashi Singh 6 years, 9 months ago
. . 6 years, 9 months ago
Posted by Yogita Malik 6 years, 9 months ago
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Yogita Malik 6 years, 9 months ago
Posted by Priya Padhi 6 years, 9 months ago
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Yogita Malik 6 years, 9 months ago
Posted by Deepali Agrawal 6 years, 9 months ago
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Posted by Sumaiya Fathima 6 years, 9 months ago
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Yogita Ingle 6 years, 9 months ago
96 = 2 × 2 × 2 × 2 × 2 × 3
21 = 7 × 3
HCF = 3
LCM = 2 × 2 × 2 × 2 × 2 × 3× 7 = 672
Posted by Pallav Singh 6 years, 9 months ago
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Posted by Saurabh Singh 6 years, 9 months ago
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Gaurav Seth 6 years, 9 months ago
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
Posted by Nikhil Sahu 6 years, 9 months ago
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Posted by Karvi Patel 6 years, 9 months ago
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Posted by Premjit Hidam 6 years, 9 months ago
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Posted by Chandan Yaralli 6 years, 9 months ago
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Yogita Ingle 6 years, 9 months ago
x + y = 5xy ........... (i)
3x + 2y = 13 xy ............ (ii)
Multiplying equation (i) by 2 and equation (ii) by 1 , we get
2x + 2y = 10xy .......... (iii)
3x + 2y = 13xy ........ (iv)
Subtracting equation (iii) from equation (iv), we get
y = 1/3
Putting y = 1/3 in (i) we get
x = 1/2
Hence, solution of the given system of equations is x=1/2, y= 1/3.</div>
Posted by Nikhil Raghuwanshi 6 years, 9 months ago
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Posted by Abhinav Agrawal 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Suppose the numerator and denominator of the fraction be x and y respectively.
Then the fraction is {tex}\frac{x}{y}{/tex}.
If 1 is added to the numerator and 1 is subtracted from the denominator, the fraction becomes 1.
Thus, we have {tex}\frac{{x + 1}}{{y - 1}} = 1{/tex}
{tex}\Rightarrow{/tex} {tex}(x + 1) = (y - 1){/tex}
{tex}\Rightarrow{/tex} {tex}x + 1 - y + 1 = 0{/tex}
{tex}\Rightarrow{/tex} {tex}x - y + 2 = 0{/tex}
If 1 is added to the denominator, the fraction becomes {tex}\frac{1}{2}{/tex}.
Thus, we have {tex}\frac{x}{{y + 1}} = \frac{1}{2}{/tex}
{tex}\Rightarrow{/tex} {tex}2x = (y + 1){/tex}
{tex}\Rightarrow{/tex} {tex}2x - y - 1 = 0{/tex}
We have two equations
{tex}x - y + 2 = 0{/tex}
{tex}2x - y - 1 = 0{/tex}
By using cross-multiplication, we have
{tex}\frac{x}{{( - 1) \times ( - 1) - ( - 1) \times 2}}{/tex} {tex} = \frac{{ - y}}{{1 \times ( - 1) - 2 \times 2}}{/tex} {tex} = \frac{1}{{1 \times ( - 1) - 2 \times ( - 1)}}{/tex}
{tex}\Rightarrow \frac{x}{{1 + 2}}{/tex} {tex}=\frac{{ - y}}{{ - 1 - 4}} = \frac{1}{{ - 1 + 2}}{/tex}
{tex}\Rightarrow \frac{x}{3} = \frac{{ - y}}{{ - 5}} = \frac{1}{1}{/tex}
{tex}\Rightarrow \frac{x}{3} = \frac{y}{5} = 1{/tex}
So, {tex}x = 3\ and\ y = 5.{/tex}
The fraction is {tex}\frac{3}{5}{/tex}.
Posted by Lakshay Kochhar 6 years, 9 months ago
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Posted by Sunil Kumar 6 years, 9 months ago
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Posted by Aryan Patel 6 years, 9 months ago
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Yogita Ingle 6 years, 9 months ago
Let three consecutive positive integers be, n, n + 1 and n + 2.
When a number is divided by 3, the remainder obtained is either 0 or 1 or 2.
∴ n = 3p or 3p + 1 or 3p + 2, where p is some integer.
If n = 3p, then n is divisible by 3.
If n = 3p + 1, ⇒ n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3.
If n = 3p + 2, ⇒ n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3.
So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.
⇒ n (n + 1) (n + 2) is divisible by 3.
Similarly, when a number is divided 2, the remainder obtained is 0 or 1.
∴ n = 2q or 2q + 1, where q is some integer.
If n = 2q ⇒ n and n + 2 = 2q + 2 = 2(q + 1) are divisible by 2.
If n = 2q + 1 ⇒ n + 1 = 2q + 1 + 1 = 2q + 2 = 2 (q + 1) is divisible by 2.
So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 2.
Hence n (n + 1) (n + 2) is divisible by 2 and 3.
∴ n (n + 1) (n + 2) is divisible by 6. </div>
Posted by Priyanshu Raj 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Length of a room {tex}= 16 m {/tex}
Breadth of a room {tex}= 13.5 m{/tex}
{tex}\therefore {/tex} Area of a room = ({tex}16{/tex} {tex}\times{/tex} {tex}13.5{/tex}) m2 {tex}= 216 {/tex}m2
Width of a carpet {tex}= 75 m {/tex}
{tex}\therefore {/tex} Length of a carpet = {tex}\frac { \text { Area of a room } } { \text { Width of a carpet } }{/tex} = {tex}\frac { 16 \times 13.5 } { 75 }{/tex} {tex}= 2.88 m{/tex}
Cost of carpet = Rs. {tex}60{/tex} per meter
{tex}\therefore {/tex} Cost of {tex}2.88 {/tex}m long carpet = Rs. {tex}60{/tex} {tex}\times{/tex} {tex}2.88 ={/tex} Rs. {tex}172.8{/tex}
Posted by Rishu Kedia 6 years, 9 months ago
- 1 answers
Yogita Ingle 5 years, 9 months ago
Let p(x) be any polynomial of degree greater than or equal to 1 and let α be any real number. If p(x) is divided by the polynomial (x - α), then the remainder is p(α).
In other words:
If the polynomial f(x) is divided by x - α then the remainder R is given by f(x) = (x - α) q(x) + R, where q(x) is the quotient and R is a constant (because the degree of the remainder is less than the degree of the divisor x - α).
Putting x = α, f(α) = (α - α)q(α) + R or f(α) = R
When the polynomial f(x) is divided by x - α, the remainder R = f(α) = value of f(x) when x is α.
Posted by Shreekant1972 Mangaligi 6 years, 9 months ago
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Mr.Poet ? _Prankster?_ Error 444? 6 years, 9 months ago
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