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
(Question 63) I have the answer in my book, but I have no idea how they got it, so any explaination would be super helpful! Than
vitfil [10]

You have to know that the graph of the arctangent function is a flat S-shaped curve that goes through (0, 0) and has asymptotes at ±π/2. The factor of 2 that multiplies it here expands it vertically so the asymptotes are at ±π. The +3 added to the x causes it to be shifted to the left by 3 units.

5 0
3 years ago
Solve for X, will mark brainliest if right
Vitek1552 [10]

Answer:

<u>x = 8</u>

Step-by-step explanation:

The sides are in proportion.

  • \frac{RG}{FG} =\frac{SH}{FH}
  • 40 / 7x + 14 = 44 / 33 + 44
  • 40 / 7x + 14 = 44/77 = 4/7
  • 40(7) = 4(7x + 14)
  • 280 = 28x + 56
  • 10 = x + 2
  • <u>x = 8</u>
3 0
2 years ago
Can someone help me please
Ymorist [56]
Add 5x + 5 and that is the bottom of it and the top stays 1
3 0
3 years ago
ROUND YOUR ANSWER TO THE NEAREST TENTH
Alenkasestr [34]

Answer:8 I think, sorry it it is wrong

Step-by-step explanation:

7 0
3 years ago
The equation y−5=−2(x−3) is in point-slope form. Which shows this equation in slope-intercept form?
MAXImum [283]

y - 5 = -2(x - 3)

Distribute -2.


y - 5 = -2x + 6

Add 5 to both sides.


y = -2x + 11

B) y = -2x + 11

4 0
3 years ago
Other questions:
  • What is the product of −214 and 212?
    11·2 answers
  • Multiply. Enter your answer in scientific notation.
    12·1 answer
  • How do you work out 2/5 of 10
    14·2 answers
  • 0.924 in expanded form anyone?
    15·2 answers
  • What is the product of 2p + q and –3q – 6p + 1?
    11·1 answer
  • Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty perso
    6·1 answer
  • Which multiple choice is it?
    6·1 answer
  • Whats 2+2???<br> Five or sometin?? hehe
    9·2 answers
  • Question 1 (Fill-In-The-Blank Worth 3 points)
    11·1 answer
  • Which best describe the relationship between the two lines describe below?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!