1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mariarad [96]
3 years ago
11

Any 10th grader solve it for 50 points​

Mathematics
1 answer:
kkurt [141]3 years ago
5 0

Answer:

\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0  is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.

Step-by-step explanation:

Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.

First term of given arithmetic progression is A

and common difference is D

ie., a_{1}=A and common difference=D

The nth term can be written as

a_{n}=A+(n-1)D

pth term of given arithmetic progression is a

a_{p}=A+(p-1)D=a

qth term of given arithmetic progression is b

a_{q}=A+(q-1)D=b and

rth term of given arithmetic progression is c

a_{r}=A+(r-1)D=c

We have to prove that

\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0

Now to prove LHS=RHS

Now take LHS

\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)

=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)

=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)

=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}

=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}

=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}

=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}

=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}

\neq 0

ie., RHS\neq 0

Therefore LHS\neq RHS

ie.,\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0  

Hence proved

You might be interested in
What is the probability that a value falls in the interval μ ± 2σ, that computes the probability P(-2 < Z < 2). Round to f
bija089 [108]

Answer:

0.9544    

Step-by-step explanation:

P(-2 < Z < 2) means that Z has mean 0 and standard deviation 2.

P(−2 < Z < 2) = F(2) - F(-2)

Using the Z - table,

F(2) = 0.9772

and F(-2) = 0.0228

Thus,

P(−2 < Z < 2) = 0.9772 - 0.0228 = 0.9544

This means that data within two standard deviation is 95%.

8 0
3 years ago
The sides of a square are increased by a scale factor of 6. The perimeter of the smaller square is 10 ft. What is the perimeter
inn [45]

Answer:

60ft

Step-by-step explanation:

I have not  done this kind of work in a while but if you scale each side of the square by 6 is should increase to a perimeter of 60ft

4 0
3 years ago
20. Determine the following product. 5g(-3g²h - 7g + 9)
soldier1979 [14.2K]
Distribute 5g to all of the terms in parentheses:

5g \times -3g^2h = -15g^3h
5g \times -7g = -35g^2
5g \times 9 = 45g

-15g^3h - 35g^2 + 45g

The answer is A.
4 0
3 years ago
How do you make -6/10 into the sum of 1
vodka [1.7K]

Answer:

depands

Step-by-step explanation:

sorry put sure yo can really just do 50 so

7 0
2 years ago
What is the prime factorization of 77 ?
n200080 [17]

Prime factorization: 77=7*11

8 0
3 years ago
Other questions:
  • 5000 sheets of paper cost $115 how much does a singcost
    12·1 answer
  • What is the range of 2,3,2
    10·1 answer
  • PLZ ANSWER BEING TIMED!!!!!!!!!! WILL MARK BRAINLIEST GIVE THANKS AND MARK 5 STARS!!!!!!!
    5·1 answer
  • PLZZZ HELP!! I WILL GIVE BRAINLIEST
    8·2 answers
  • Forty-two people charter a bus for $788. Estimate the amount each person pays.<br> Your answer
    12·1 answer
  • He was a newcomer in the land, a chechaquo, and this was his first winter. The trouble with him was that he was without imaginat
    8·1 answer
  • All you need is in the photo please
    15·1 answer
  • 40 POINTS THERE IS MORE THAN 1 ANSWER BRAINLIEST IF CORRECT
    7·1 answer
  • Solve for t.<br> 45 = 5t + 45<br> Answer:<br> Submit Answer
    9·2 answers
  • Find the missing side of the triangle
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!