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Ask QuestionPosted by Aavani Vs 5 years, 3 months ago
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Posted by Suraj Ku 5 years, 3 months ago
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Gaurav Seth 5 years, 3 months ago
To prove:
Solution:
Given: The sum of first ‘n’ terms of three AP's are . The ‘first term’ of each is 5 and their common differences are 2, 4 and 6 respectively.
Formula of summation of an A.P
whereas = Summation till n terms.
a = First term of sequence
d = Common Difference
Now, using this formula, we get
Thus, we need to add to prove that
Thus, .
Hence proved.
Posted by Altaf Ahmad Sofi 5 years, 3 months ago
- 2 answers
Posted by Altaf Ahmad Sofi 5 years, 3 months ago
- 1 answers
Posted by Nk Jha Jha 5 years, 3 months ago
- 1 answers
Gaurav Seth 5 years, 3 months ago
AAA similarity theorem or criterion:
If the corresponding angles of two triangles are equal, then their corresponding sides are proportional and the triangles are similar
In ΔABC and ΔPQR, ∠A = ∠P , ∠B = ∠Q , and ∠C = ∠R then AB PQ = BC QR = ACPRand ΔABC ∼ ΔPQR.
Given: In ΔABC and ΔPQR, ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R.
To prove: AB PQ = BC QR = ACPR
Construction : Draw LM such that PL AB = PM AC .
Proof: In ΔABC and ΔPLM,
AB = PL and AC = PM (By Contruction)
∠BAC = ∠LPM (Given)
∴ ΔABC ≅ ΔPLM (SAS congruence rule)
∠B = ∠L (Corresponding angles of congruent triangles)
Hence ∠B = ∠Q (Given)
∴ ∠L = ∠Q
LQ is a transversal to LM and QR.
Hence ∠L = ∠Q (Proved)
∴ LM ∥ QR
PL LQ = PM MR
LQ PL = MR PM (Taking reciprocals)
LQ PL + 1 = MR PM + 1 (Adding 1 to both sides)
LQ+PL PL = MR+PM PM
PQ PL = PR PM
PQ AB = PR AC (AB = PL and AC =PM)
AB PQ = AC PR (Taking Reciprocals) ............... (1)
AB PQ = BC QR
AB PQ = AC PR = BC QR
∴ ΔABC ~ ΔPQR
Posted by Himanshu Jagne 5 years, 3 months ago
- 1 answers
Yogita Ingle 5 years, 3 months ago
Let a be the amount of air initially Amount of air remaining after 1st pump =a –(a/4)=3a/4
Amount of air remaining after 2nd pump= (3a/4) – (1/4)(3a/4)=9a/16
Amount of air remaining after 3rd pump= (9a/16) – (1/4)(9a/16)=27a/64
So the series is like
a,3a/4,9a/4,27a/64……..
Difference Ist and second term=-a/4
Difference between Second and Third term= -3a/16
So difference is not constant
So it is not Arithmetic Progression
Posted by Krishna Gond 5 years, 3 months ago
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Posted by Aishnawaz Aishnawaz 5 years, 3 months ago
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Posted by Vishalini Singar 5 years, 3 months ago
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Rakshitha M 5 years, 3 months ago
Posted by Harsha Jv 5 years, 3 months ago
- 1 answers
Gaurav Seth 5 years, 3 months ago
We have a circle of radius 5 cm with a chord of length 8 cm.
We have to find length TP.
We have,
OP=5 cm
PM=4 cm .......(perpendicular from the centre divides the chord)
OM=3 cm .......(by using Pythagorean triplet)
Let 
and TP be x.
Use trigonometric ratio in the triangle PMO and POT we get,
Therefore, TP =6.66 cm
Posted by Sumaila Ali Choudhary??? 5 years, 3 months ago
- 4 answers
Posted by Sheryn William 5 years, 3 months ago
- 1 answers
Yogita Ingle 5 years, 3 months ago
side of cube (a)= 1 cm
volume of cube = a³ = 1 cm³ = 1000 mm³
volume of material remains same
So,
volume of cube = volume of wire
volume of wire = π r² × h
1000 mm³ = π × (4/2)² × h
h = 1000/[ π × 4]
h = 250/π mm = 25/π cm
Posted by Sakthi Dharshni 19 Shasmitha 5 years, 3 months ago
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Posted by Surya Pratap Singh Chauhan 5 years, 3 months ago
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Namrata Jindal 5 years, 3 months ago
Posted by Puranjay Vyas 5 years, 3 months ago
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Amit Kumar Chaurasia 5 years, 3 months ago
Posted by Rishi Kumar 5 years, 3 months ago
- 1 answers
Gaurav Seth 5 years, 3 months ago
Let the numbers be a - d, a, a + d which are in AP.
(a - d) + (a) + (a + d) = 27 .........(1)
(a - d)(a)(a + d) = 405 ..........(2)
(1) => 3a = 27
a = 9
(2) => (a2 - d2)(a) = 405
[(9)2 - d2] (9) = 405
(81 - d2) (9) = 405
729 - 9d2 = 405
9d2 = 729 - 405
9d2 = 324
d2 = 36
d = 6
Now, substitute the values in the 1st equation.
(a-d) = 9 - 6 = 3
a = 9
(a+d) = 9 + 6 = 15
Hence the numbers are 3, 9 and 15.
Posted by Shivani Chaudhary 5 years, 3 months ago
- 2 answers
Shivani Chaudhary 5 years, 3 months ago
Gaurav Seth 5 years, 3 months ago
3x+2y=11
2x+3y=4
by adding them
5x+5y=15
x+y=3
x=3-y
put the value of x
3x+2y=11
3(3-y)+2y=11
9-3y+2y=11
9-y=11
-y=11-9
-y=2
y=-2
put the value of y
x=3-y
x=3-(-2)
x=3+2
x=5
hence x=5 and y=-2
Posted by Kshitija Kadam 5 years, 3 months ago
- 0 answers
Posted by Sudhanshu Katara 5 years, 3 months ago
- 1 answers
Posted by Adithi B N 5 years, 3 months ago
- 1 answers
Yogita Ingle 5 years, 3 months ago
x + y = a + b …(i)
ax – by = a2 – b2…(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply equation (i) by b, so that variable y in both the equations have same coefficient.
Recalling equations (i) & (ii),
x + y = a + b [×b
ax – by = a2 – b2
⇒ bx + ax = ab + a2
⇒ (b + a)x = a(b + a)
⇒ x = a
Substitute x = a in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (i), we get
a + y = a + b
⇒ y = b
Hence, we have x = a and y = b.
Posted by Harsh Rathore 5 years, 3 months ago
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Posted by Rahul Soni 5 years, 3 months ago
- 1 answers
Manju Angadi 5 years, 3 months ago
Posted by Eshna Riwar 5 years, 3 months ago
- 1 answers
Nivi :) 5 years, 3 months ago
Posted by Himanshu Chaudhary 5 years, 3 months ago
- 1 answers
Posted by Shivam Jaiswal 5 years, 3 months ago
- 1 answers
Amit Kumar Chaurasia 5 years, 3 months ago
Posted by Ankit Singh 5 years, 3 months ago
- 1 answers
Posted by Sumaila Ali Choudhary??? 5 years, 3 months ago
- 1 answers
Gaurav Seth 5 years, 3 months ago
Solution:
an = 2n + 3
n = 1
an = 2n + 3
a1 = 2(1) + 3
a1 = 2 + 3
a1 = 5
n = 2
an = 2n + 3
a2 = 2(2) + 3
a2 = 4 + 3
a2 = 7
n = 3
an = 2n + 3
a3 = 2(3) + 3
a3 = 6 + 3
a3 = 9
n = 4
an = 2n + 3
a4 = 2(4) + 3
a4 = 8 + 3
a4 = 11
Posted by Arnav Kumar 5 years, 3 months ago
- 1 answers
Prajwal Mehra 5 years, 3 months ago
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Gaurav Seth 5 years, 3 months ago
The point P(0,9) is equidistant from the points A(6,5) and B(-4,3).
Step-by-step explanation:
Let the point on y axis is P(0,y) which is equidistant from the points A(6,5) and B(-4,3). The distance between PA is equal to PB such that,
On squaring,
So, the point P(0,9) is equidistant from the points A(6,5) and B(-4,3).
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