CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

The given point is P (4, -3).
Distance of point P from x-axis is -3 units.
Distance of point P from y-axis is 4 units.
Distance of point P from origin = OP, where O is the origin.
From P draw line A perpendicular to x-axis.
You can observe that OAP is a right angled triangle with OA = 4 units, AP = -3 units.
So, using Pythagoras theorem,
OP² = 4² + (-3)² = 25
=> OP = 5 units
Hence, the distance of point P from origin is 5 units.

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Pragati Jain 6 years, 2 months ago

5unit

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The two positive integers p and q can be expressed as p = xy4 and q =x² y² , where x and y are prime numbers. Find hcf(p,q) and Kim (p, q)

Posted by Nandhu Siva 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Nandhu Siva 6 years, 2 months ago

The two positive integers p and q can be expressed as p =q can be expressed as p =q xy4 and q = x²y²,where x and y are prime numbers. Find hcf(p,q) and lcm(p,q)

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3 digits divisible by 8

Posted by Shree Ravi 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

? ? 6 years, 2 months ago

104 is the first 3 digit no. which is divisible by 8.

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? ? 6 years, 2 months ago

Ans is :-104

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Diffen Euclid division lemma

Posted by Meenaxi Misal 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 2 months ago

Theorem (Euclid’s Division Lemma):

For a pair of given positive integers ‘a’ and ‘b’, there exist unique integers ‘q’ and ‘r’ such that

a=bq+ra=bq+r, where 0≤r<b0≤r<b

Explanation:

Thus, for any pair of two positive integers a and b; the relation

a=bq+ra=bq+r, where 0≤r<b0≤r<b

will be true where q is some integer.

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Prove that underroot 2 is an irrational number

Posted by Kashish Sikka 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 2 months ago

Let √2 be a rational number

Therefore, √2= p/q [ p and q are in their least terms i.e., HCF of (p,q)=1 and q ≠ 0

On squaring both sides, we get
p²= 2q² ...(1)
Clearly, 2 is a factor of 2q²
⇒ 2 is a factor of p² [since, 2q²=p²]
⇒ 2 is a factor of p

Let p =2 m for all m ( where m is a positive integer)

Squaring both sides, we get
            p²= 4 m²                                                                                          ...(2)
From (1) and (2), we get
           2q² = 4m²      ⇒      q²= 2m²
Clearly, 2 is a factor of 2m²
⇒       2 is a factor of q²                                                      [since, q² = 2m²]
⇒       2 is a factor of q

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number.

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If secA+tan A=p Prove that sin A = psquare-1 divided by p square +1

Posted by Thejaswini Prakash 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 2 months ago

SecA+tanA=p ----------------------------(1)
We know that,
sec²A-tan²A=1
or, (secA+tanA)(secA-tanA)=1
or, p(secA-tanA)=1
or, secA-tanA=1/p -----------------------(2)
Adding (1) and (2) we get,
2secA=p+1/p
or, secA=(p²+1)/2p
∴, cosA=1/secA=2p/(p²+1)
∴, sinA=√(1-cos²A)
=√{1-4p²/(p²+1)²
=√{(p²+1)²-4p²}/(p²+1)²
=√(p⁴+2p²+1-4p²)/(p²+1)
=√(p²-1)²/(p²+1)
=(p²-1)/(p²+1) (Proved)