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Ask QuestionPosted by Mayank Kumar 4 years, 3 months ago
- 1 answers
Posted by Harshitha Dinesh 4 years, 3 months ago
- 0 answers
Posted by Chinnu B 4 years, 3 months ago
- 1 answers
Gaurav Seth 4 years, 3 months ago
∵ In ∆ABC,
AB = AC
∴ ∠B = ∠C ...(1)
| Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
| Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
| ∵ ∠A = 90° (given)
⇒ ∠B + ∠C = 90° ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.
Posted by Aayush Gaikwad 4 years, 3 months ago
- 2 answers
Posted by Tejvinder Yadav 4 years, 3 months ago
- 1 answers
Gaurav Seth 4 years, 3 months ago
Let ΔABP and a parallelogram ABCD be on the same base AB and between the same parallels AB and PC.
To Prove : ar( ΔPAB ) = (1/2)ar( ABCD)
(here, ar = area; written in short)
Draw BQ ||AP to obtain another parallelogram.ABQP and ABCD are on the same base AB and between the same parallels AB and PC.
There fore, ar(ABQP) = ar(ABCD)
But ΔPAB ≅ ΔBQP( Diagonals PB divides parallelogram ABQP into two congruent triangles.
So ar (PAB) = ar(BQP) -----------(2)
∴ ar (PAB) = (1/2)ar(ABQP) -----------------(3) [ from (2)]
This gives ar (PAB) = (1/2)ar(ABCD) [ from (1) and (3)]
Posted by Pankul Khurana 4 years, 3 months ago
- 1 answers
Gaurav Seth 4 years, 3 months ago
Apply remainder theorem
=>7 + 3x =0
=> 3x = - 7
=> x = - 7/3
Replace x by - 7/3 we get
=>3x3 + 7x
=>3(-7/3)3 + 7(-7/3)
=>3(-343/27) – 49/3
=> (-343/9) – 49/3
This value is not equal to 0
So that 7 + 3x is not a factor of expression 3x3 + 7x
Posted by Priyashi Panchal 4 years, 3 months ago
- 0 answers
Posted by Brajesh Kumar 4 years, 3 months ago
- 1 answers
Kartikeya Srivastav 4 years, 3 months ago
Posted by Aakanksha Salve 4 years, 3 months ago
- 0 answers
Posted by Arkesh Kumar 4 years, 3 months ago
- 2 answers
Posted by Adarsh Kumar 4 years, 3 months ago
- 1 answers
Posted by Almi Aami 4 years, 3 months ago
- 2 answers
Yogita Ingle 4 years, 3 months ago
95 × 96
= (95.5-0.5)(95+0.5)
= (95.5)2- (0.5)2
= 9120.25 - 0.25
= 9120
Posted by Sara Biju 4 years, 3 months ago
- 3 answers
Sujita N B 4 years, 3 months ago
Yogita Ingle 4 years, 3 months ago
6√3+5√12
= 6√3+5√4× 3
=6√3 + 10√3
= (6 + 10) √3
= 16 √3
Posted by Laxmi Kaushik. 4 years, 3 months ago
- 0 answers
Posted by Laxmi Kaushik. 4 years, 3 months ago
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Posted by Drishti Garg 4 years, 3 months ago
- 5 answers
Kartikeya Srivastav 4 years, 3 months ago
Posted by Anuj Patwa 4 years, 3 months ago
- 1 answers
Kartikeya Srivastav 4 years, 3 months ago
Posted by Hakeem Urva Tul Wusqa 4 years, 3 months ago
- 1 answers
Gaurav Seth 4 years, 3 months ago
Let O and O’ be the centres of the circles of radii 5 cm and 3 cm respectively and let PQ be their common chord.
OP = 5 cm, O’P = 3 cm, OO’ = 4 cm.
Let OL = x, so LO’ = 4 - x
Let PQ = y, so PL = y/2
In right triangle OLP,
OL2 = (OP2 – LP2) = 52 – (y/2)2
=> x2 = 25 – y2/4 …(i)
In right triangle O’LP, O’L2 = (32 – y2/4)
(4 – x)2 = 9 – y2/4 …(ii)
From (i) and (ii) we get
x2 – 16 + 8x – x2 = 25 – y2/4 – 9 + y2/4
=> 8x =32
=> x = 4
From equation (i)
16 = 25 – y2/4 => y2/4 = 9 => y2 = 36 => y = 6
Thus, the length of the common chord is 6 cm.
Posted by Om Patil 4 years, 3 months ago
- 2 answers
Posted by Kartikeya Srivastav 4 years, 3 months ago
- 0 answers
Posted by Mahesh Rathore 4 years, 3 months ago
- 1 answers
Aman Maurya 4 years, 3 months ago
Posted by Shruti Dabral 4 years, 3 months ago
- 0 answers
Posted by Anil Kumar 4 years, 3 months ago
- 2 answers
Posted by Kartikeya Srivastav 4 years, 3 months ago
- 1 answers
Gaurav Seth 4 years, 3 months ago
a² - b⁴ = 2009
a² - b⁴ = (a + b²)(a - b²)
Now, we have to find out all the factors of 2009.
Factors of 2009 are = 1, 7, 41,49, 287 and 2009
Now, we have to use the difference of squares of factorization to obtain (a + b²)(a - b²) = 2009
The prime factorization of 2009 is 7²*41.
If we choose two factors 'x' and 'y' such that xy = 2009,
a + b² = x and a - b² = y, then 2b² = x - y.
If x = 2009, then y = 1 and 2b² = 2008,
then, b² = 2008/2
b = √1004 which is not and integer.
Now, if x = 287, then y = 7 and 2b² = 280
then, b² = 280/2
b = √140 which is also not an integer.
Now, if x = 49, then y = 41 and 2b² = 8
then b² = 8/2
b = √4
b = 2
Now, putting the value of b =2 in a² - b⁴ = 2009
⇒ a² - 2⁴ = 2009
⇒ a² - 16 = 2009
⇒ a² = 2009 + 16
⇒ a² = 2025
⇒ a = √2025
⇒ a = 45
So, the value of a and b is 45 and 2 respectively.
Posted by Kartikeya Srivastav 4 years, 3 months ago
- 1 answers
Posted by Neelam Patle 4 years, 3 months ago
- 0 answers
Posted by Kartikeya Srivastav 4 years, 3 months ago
- 2 answers
Kartikeya Srivastav 4 years, 3 months ago
Gaurav Seth 4 years, 3 months ago
Trapezium
A trapezium has one pair of sides parallel while the other isn’t. A trapezium is basically a triangle with the top sliced off. The parallel sides of this quadrilateral are called the base and to calculate the height you need to draw a perpendicular from one parallel side to other.
The formula for area of a trapezium is,
Area of Trapezium= [(a+b)h]/2
Posted by Sara Biju 4 years, 3 months ago
- 5 answers
Gaurav Seth 4 years, 3 months ago
3+✓5 / 3 - ✓5
=> 3 + ✓5 / 3 - ✓5 × 3 + ✓5/ 3 + ✓5
=> ( 3 + ✓5) ( 3 + ✓5) / ( 3 - ✓5) ( 3 + ✓5)
=> ( 3 + ✓5)² / (3)² - ( ✓5)²
=> (3)² + ( ✓5)² + 2 × 3 × ✓5 / 9 -5
=> 9 + 5 + 6✓5 / 4
=> 14 + 6✓5/4
=> 2 ( 7 + 3✓5 ) /4
=> 7 + 3✓5/2
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Yogita Ingle 4 years, 3 months ago
Let p(x) = x3 + 13x2 + 32x + 20
p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0
Therefore (x + 1) is a factor of p(x).
On dividing p(x) by (x + 1) we get
p(x)
(x + 1) = x2 + 12x + 20
Thus,
x3 + 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)
= (x + 1) (x2 + 10x + 2x + 20)
= (x + 1)[x(x + 10) + 2(x + 10)]
= (x + 1) (x +2) (x + 10)
Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x +2) (x + 10).
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