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Gaurav Seth 3 hours ago
Let speed of boat in still water be x km/h and speed of stream be y km/h.
Speed upstream= (x - y) km/h
Speed downstream= (x + y) km/h
On subtracting, we get,
On solving, we get,
Speed of boat in still water = 8 km/h
And, Speed of stream = 3 km/h
Posted by Jaya Shree Meenakshi 4 hours ago
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Yogita Ingle 3 hours ago
Euclid division lemma:-
a=bq+r
First find the HCF of 693 and 567,
693=567(1)+126
567=126(4)+63
126=63(2)+0
HCF of 693 and 567 is 63.
Now find the HCF of 63 and 441,
441=63(7)+0
The HCF of 63 and 441 is 63.
Therefore, the HCF of 441,567 and 693 is 63.
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Gaurav Seth 4 hours ago
Q: Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8
Let x be any positive integer. Then, it is of the form 3q or, 3q + 1 or, 3q + 2.
So, we have the following cases :
Case I : When x = 3q.
then, x3 = (3q)3 = 27q3 = 9 (3q3) = 9m, where m = 3q3.
Case II : When x = 3q + 1
then, x3 = (3q + 1)3
= 27q3 + 27q2 + 9q + 1
= 9 q (3q2 + 3q + 1) + 1
= 9m + 1, where m = q (3q2 + 3q + 1)
Case III. When x = 3q + 2
then, x3 = (3q + 2)3
= 27 q3 + 54q2 + 36q + 8
= 9q (3q2 + 6q + 4) + 8
= 9 m + 8, where m = q (3q2 + 6q + 4)
Hence, x3 is either of the form 9 m or 9 m + 1 or, 9 m + 8.
Posted by Jo Hosakke Kar Lo 😁😁🤣🤣✌️ 7 hours ago
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Gaurav Seth 6 hours ago
Answer:
Step-by-step explanation:
we have to find the 5 irrational number which are lying between 4 and 5 in radical form
Irrational numbers are those real numbers that cannot be written as a simple fraction. These are non-terminating and non-repeating.
All the above five numbers are non-terminating and non-repeating.
Posted by Jo Hosakke Kar Lo 😁😁🤣🤣✌️ 7 hours ago
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Gaurav Seth 6 hours ago
Total pens=1001
Total pencils=910
we need to find maximum no.of students among whom 1001 pens and 910 pencils can be distributed in such a way that each students get same no.of pens and pencils.
Then we need to find HCF of 1001 and 910
Prime factorization of,
1001=7×11×13
910=2×5×7×13
HCF=product of commom prime factor of least power
HCF=7×13=91
Here HCF of 1001 and 910 is 91.
Hence among 91 students 1001 pens and 910 pencils can be distributed such that each student get same no.of pens and pencils.
Posted by Høñéy Khäñ 8 hours ago
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Posted by Krishan Kadian Kadian 11 hours ago
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Yogita Ingle 11 hours ago
2x2 -5x + 3
= 2x2 - 2x -3 x + 3
= 2x(x - 1) - 3 ( x - 1)
= (x -1) (2x - 3)
Posted by Yogesh Meena 12 hours ago
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Gaurav Seth 12 hours ago
Question : Find the series if an=9−5n
Given
an=9−5n
a1=9−5=4
a2=9−10=−1
a3=9−15=−6
∴ The series is 4,−1,−6,−11....
Posted by Rani Jijo 12 hours ago
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Gaurav Seth 12 hours ago
Let’s assume the two numbers be x and y. And also assume that x is greater than or equal to y.
So as per the question, we can write the sum of the two numbers as
x + y = 1000 ……….. (i)
Again it’s given that, the difference between the squares of the two numbers, thus writing it
x2 – y2 = 256000
⇒ (x + y) (x – y) = 256000
⇒ 1000(x - y) = 256000
⇒ x – y = 256000/1000
⇒ x – y = 256 ………….. (ii)
By solving (i) and (ii), we can find the two numbers
On adding the equations (i) and (ii), we get;
(x + y) + (x - y) = 1000 + 256
⇒ x + y + x – y =1256
⇒ 2x = 1256
⇒ x = 1256/ 2
⇒ x = 628
Now, putting the value of x in equation (i), we get
628 + y =1000
⇒ y = 1000 – 628
⇒ y = 372
Hence, the two required numbers are 628 and 372.
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Yogita Ingle 1 day, 6 hours ago
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.
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Aditya Raj an hour ago
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