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Show that the square of any positive integer is of the formof 3m or 3m+1 for some integer m.

Posted by Neelam Dubey 6 years, 11 months ago

2 answers

Ram Kushwah 6 years, 11 months ago

As per Euclid's Division Lemma
If a & b are 2 positive integers, then
a = bq + r {tex}0\;\leq b<r{/tex}
let b=3
hence r=0,1,2
If r=0

{tex}\begin{array}{l}a^2=(3q)^2=3x3q^2=3m\;(m=3q^2)--(1)\\if\;r=1\;then\;\\a^2=(3q+1{)^2=9q^2+6q+1=3}(3q^2+2q)+1=3m+1\;--(2)\;(m=3q^2+2q)\;---(2)\\if\;r=2\\a^2=(3q+2)^2=9q^2+12q+4=3(3q^2+4q+1)+1=3m+1--(3)\;\;(m=3q^2+4q+1)\end{array}{/tex}

From (1) ,(2) and (3)

square of any positive integer a is in the form of 3m or 3m +1

1Thank You

Rakhi Yadav 6 years, 11 months ago

is m 3m+1 ka hole square lage ga or jo bahar aye ga usko m ke equal rkh na h or let m q lena h

2Thank You

ANSWER

Can two numbers have 16 as their HCF and 380 as their LCM ? Give reason

Posted by Shivani Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 11 months ago

HCF of two numbers is a factor of the LCM of those numbers.
Thus, we cannot have two numbers whose HCF is 16 and LCM is 380.
Because, when we divide 380 by 16, we get a remainder of 12.
Thus, 16 is not a factor of 380.
Hence, we cannot have two numbers whose HCF is 16 and LCM is 380.

2Thank You

Anshika & Aliens???? 6 years, 11 months ago

HCF of two numbers should be the factor of LCM of those numbers. But, 16 is not a Factor of 380. Hence, two numbers can not have their HCF and LCM as 16 and 380

2Thank You

ANSWER

28.5✓3 - 9.5✓3 = ??

Posted by Anshika & Aliens???? 6 years, 11 months ago

CBSE > Class 10 > Mathematics

5 answers

Ram Kushwah 6 years, 11 months ago

Anshika,

The answer is

{tex}\begin{array}{l}28.5\sqrt3-9.5\sqrt3\\=9.5\sqrt3(3-1)\\=2\times9.5\sqrt3\\=19\sqrt3\end{array}{/tex}

Here no need to cut {tex} \sqrt 3{/tex} ,You can leave the answer as it.

1Thank You

Puja Sahoo? 6 years, 11 months ago

Root 3( 28.5 - 9.5) = 19 root 3.........???

2Thank You

Anshika & Aliens???? 6 years, 11 months ago

Par kese puja ✓3 - ✓3 cut nhi hoga kya bolo

1Thank You

Puja Sahoo? 6 years, 11 months ago

19 root 3....

3Thank You

Anshika & Aliens???? 6 years, 11 months ago

Are koi to bata do answer 19 hoga ki 19✓3 ??????? please batado

1Thank You

ANSWER

What is substitution reaction Describe with example

Posted by Ricky Roy 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 11 months ago

A substitution reaction is a reaction in which an atom or a group of atom substitutes another atom in an organic compound. For example, chlorination of alkanes occurs by substitution of H-atom in alkane by Cl-atom.

The reaction of magnesium with copper chloride
Mg + CuCl₂ → MgCl₂ + Cu

1Thank You

Anshika & Aliens???? 6 years, 11 months ago

A substitution reaction is a type of chemical reaction where an atom or functional group of a molecule is replaced by another atom or functional group. Examples: CH3Cl reacted with a hydroxy ion (OH-) will produce CH3OH and chlorine

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ANSWER

In ∆ABC, angle abc = 45°.prove that AC² = AB² + BC² - 4ar(∆abc).

Posted by Sandeep Krishnaa 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 11 months ago

Angle ABC measures 45° (given). Hence angle OAB will also be 45°
As a result x = h

Now the area of triangle ABC = 1/2(BC)(h) = 1/2(BC)(x) ; since h = x,
Or we can write BC = 2(Area of Triangle ABC)/x ----------------(i)

We can also write AC² = h² + y²
But y is nothing but (BC - x)

So we can write AC² = h² + (BC - x)²

Simplifying this we get,
AC² = h² + BC² + x² - 2.x.BC
Now x² + h² = AB² (by Pythagoras theorem for triangle AOB)

Hence AC² = AB² + BC² -2(x)(BC)
Substituting the value of BC obtained from (i), we get
AC² = AB² + BC² - 2(x)(2Area of Triangle ABC)/x

Simplifying this we get:
AC² = AB² + BC² -4.Area of Triangle ABC

0Thank You

ANSWER

How can we find the median from the cumulative distribution of more than type?In NCERT book a such table is given and written that median can be calculated from both types of tables but it explained only how to calculate median from cf of less than type distribution

Posted by Maria Smith 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Anshika & Aliens???? 6 years, 11 months ago

Using median formula

2Thank You

ANSWER

If s1=n ,s2=2n , and s3=3n than prove that s3=3 (s2-s1)

Posted by Ambalal Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Anshika & Aliens???? 6 years, 11 months ago

Let ‘a’ be the first term of the AP and ‘d’ be the common difference S1 = (n/2)[2a + (n – 1)d] --- (1) S2 = (2n/2)[2a + (2n – 1)d] = n[2a + (n – 1)d] --- (2) S3 = (3n/2)[2a + (3n – 1)d] --- (3) Consider the RHS: 3(S2 – S1) = S3 = L.H.S ∴ S3 = 3(S2 - S1) .

1Thank You

ANSWER

What is the value of root 2

Posted by Rajdeep Routh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Rajdeep Routh 6 years, 11 months ago

1.414

2Thank You

ANSWER

A two digit number is such that the product of its digits is 18 .when 63 is subtracted from the number , the digit interchange their places find the number .

Posted by Lavkush Patel 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Saurabh Kesarwani 6 years, 11 months ago

Let the tens digit &unit digit be x&y Then xy=18=>y=18/x.....1 And(10x+y)-63=10y+x =>9x-9y=63 =>x-y=7........2

3Thank You

ANSWER

What is the formula of rectangle

Posted by Anamika Dubey 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Bharat Barot 6 years, 11 months ago

1/2(product of it diagonals)

1Thank You

Ashish Kumar 6 years, 11 months ago

Area=l×b, perimeter =2(l+b)

2Thank You

Anil Jadon 6 years, 11 months ago

Two opposite sides of equal length + two opposite sides of equal length = rectangle

4Thank You

ANSWER

Prove pythagorus theorm

Posted by Aakash Sharma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Vijay Vijay 6 years, 11 months ago

One angle 90 and hypotenuse is longest side and one side

1Thank You

ANSWER

How solve the prove questions of trigonometry it is so difficult to solve. And there is so many identities

Posted by Satyam Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Bharat Barot 6 years, 11 months ago

If u don't understand anything conbert all things in sin and cos

0Thank You

Drashti Vaish 6 years, 11 months ago

Yes do practise...only

0Thank You

Satyam Raja 6 years, 11 months ago

Just practise more and you will start feeling trigonometry easy

1Thank You

ANSWER

Chapter Weightage of maths

Posted by Sania Sharma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Aryan Khare 6 years, 11 months ago

Ch 1........6marks Ch 2,3,4,5......20 marks Ch 6,10,11.......15 marks Ch 7......6 marks Ch 8,9........12 marks Ch 12,13......10 marks Ch 14,15........11marks

2Thank You

ANSWER

Sum of the areas of two squares is 468m^2. If the difference of their perimeter is 24m. Find the sides of the two squares. PLZ SOLVE IT

Posted by Jot Virk?♠ 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Sarthak Paliwal 6 years, 11 months ago

Let side of first square be x Side of another square be y Perimeter of one square - perimeter of another =24 4x-4y=24 X-y=6 Y=x-6 Now. ar of first square + area of another =468 X^2 +y^2=468 Here, y can be written as x-6 X^2 +(x-6)^2=468 ??After solving it you will get answer

2Thank You

ANSWER

The perimeters of two similar triangle are 40cm and 50cm respectively. Find the ratio of the area of first to the area of second triangle.

Posted by Deepak Shukla 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Harsh Agrawal 6 years, 11 months ago

The answer is 16/25

0Thank You

Joel Rufus 6 years, 11 months ago

I dont know

1Thank You

ANSWER

P is the midpoint of an arc QPR of a circle. Show that the tangent at P is parallel to the chord QR.

Posted by Deepak Shukla 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

can two numbers have18 as their HCF and 380 as their LCM ? Give resion.

Posted by Roshan Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Puja Sahoo? 6 years, 11 months ago

Noooo, kyunki H.C.F ko L.C.M ka factor hona chahiye bt here 18 is nt a factor of 380........

4Thank You

ANSWER

Compartment question paper 2018

Posted by Sumit Rao 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Drashti Vaish 6 years, 11 months ago

Check on the internet

0Thank You

ANSWER

SecA+tanA=x then prove sinA =x sqare -1divided by x sqare+1

Posted by Anshuman Sharma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Sri Kumar 6 years, 11 months ago

SecA+tanA=X; secA-tanA=1/x adding we get 2secA=x+1/x>>>>secA=x square+1 divide 2 x that is cosA=2x/x square+1 i.e sinA=√1- cosA^

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ANSWER

Some students planned a picnic.The total budget for food was ₹2000.But 5 students failed to attend the picnic and thus the cost of food for each member increased by ₹20.how many students attended the picnic and how much did each student pay for the food?

Posted by Sri Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Puja Sahoo? 6 years, 11 months ago

20 students attended the picnic and paid 100 rupees each for food.

3Thank You

Sri Kumar 6 years, 11 months ago

Please any one given answer

1Thank You

ANSWER

4 x square + 3 X + 5

Posted by Biren Bhatra 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Abhinandan Gouli 6 years, 11 months ago

Is it 4x^2 + 3x + 5 ?

0Thank You

ANSWER

??CHALLENGE?? U CAN IMAGINE ANSWER BUT CAN'T SOLVE THIS QUESTIONIN A PROPER WRITING WAY //// In a class there are 48 students and regular students are more than irregular than .If 2 irregular students be regular the product of the two types of student be 380 find the number of each type of students .

Posted by Fully Danger 6 years, 11 months ago

CBSE > Class 10 > Mathematics

5 answers

Puja Sahoo? 6 years, 11 months ago

Bhai, bt eq to x square + 44x - 268=0 ani chahiye

3Thank You

Fully Danger 6 years, 11 months ago

Niche galat hai equation Ye hai 44x-x square -284=0

2Thank You

Fully Danger 6 years, 11 months ago

1Thank You

Fully Danger 6 years, 11 months ago

Ye equation aa rhai hai 44x-x square+92-2x

1Thank You

Puja Sahoo? 6 years, 11 months ago

Let, no. of regular students be x and irregular will be 48-x. Now, if 2 irregular students became regular, so regular students------> x+2 and irregular students--------> 48-x-2. --> 46-x. Now, A.T.Q.......(x+2)(46-x)=380.........solve this the answer will be regular students 36, and irregular students 12.........as the value of x yu will get 36.

2Thank You

ANSWER

Find the zeros of the polynomial 4xsquare - 4x+1

Posted by Shivam Shivam 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Riya Pal 6 years, 11 months ago

4xsquare -2x -2x +1=0 2x(2x-1) -1(2x-1)=0 (2x-1)(2x-1)=0 2x-1=0,2x-1=0 X=1/2, X=1/2

0Thank You

ANSWER

SecA=2 X + 1 by 4 x prove that secant theta + tangent theta is equal to 2 x 2 x

Posted by Anshuman Sharma 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

By the given condition of question
{tex}\sec \theta = x + \frac { 1 } { 4 x }{/tex}
{tex}\therefore \quad \tan ^ { 2 } \theta = \sec ^ { 2 } \theta - 1{/tex}
{tex}\Rightarrow \quad \tan ^ { 2 } \theta = \left( x + \frac { 1 } { 4 x } \right) ^ { 2 } - 1 = x ^ { 2 } + \frac { 1 } { 16 x ^ { 2 } } + \frac { 1 } { 2 } - 1 = x ^ { 2 } + \frac { 1 } { 16 x ^ { 2 } } - \frac { 1 } { 2 } = \left( x - \frac { 1 } { 4 x } \right) ^ { 2 }{/tex}
{tex}\Rightarrow \quad \tan \theta = \pm \left( x - \frac { 1 } { 4 x } \right){/tex}
{tex}\Rightarrow \quad \tan \theta = \left( x - \frac { 1 } { 4 x } \right) \text { or, } \tan \theta = - \left( x - \frac { 1 } { 4 x } \right){/tex}
CASE 1: When {tex}\tan \theta = - \left( x - \frac { 1 } { 4 x } \right) :{/tex} In this case,
{tex}\sec \theta + \tan \theta = x + \frac { 1 } { 4 x } + x - \frac { 1 } { 4 x } = 2 x{/tex}
CASE 2: When {tex}\theta = - \left( x - \frac { 1 } { 4 x } \right) :{/tex} In this case,
{tex}\sec \theta + \tan \theta = \left( x + \frac { 1 } { 4 x } \right) - \left( x - \frac { 1 } { 4 x } \right) = \frac { 2 } { 4 x } = \frac { 1 } { 2 x }{/tex}
Hence, {tex}\sec \theta + \tan \theta = 2 x \text { or } , \frac { 1 } { 2 x }{/tex}