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faust18 [17]
3 years ago
13

If the 9th term of an ap is 1/7 and the 7th term os 1/9 find the 63rd term

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
5 0

Answer:

a_{63} = 1

Step-by-step explanation:

The n th term of an arithmetic progression is

a_{n} = a + (n - 1)d

where a is the first term and d the common difference

use the 9 th term and 7 th term to find a and d

a_{9} = a + 8d = \frac{1}{7} → (1)

a_{7} = a + 6d = \frac{1}{9} → (2)

Subtract (2) from (1) term by term

2d = \frac{2}{63} ⇒ d = \frac{1}{63}

Substitute this value into (2) and solve for a

a + \frac{6}{63} = \frac{1}{9}

a = \frac{1}{9} - \frac{6}{63} = \frac{1}{63}

Hence

a_{63} = \frac{1}{63} + \frac{62}{63} = 1


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I really need help with this
aniked [119]

Answer:

5√202

Step-by-step explanation:

By Pythagoras theorem,

x^2 = 45^2 + 55^2

= 2025 + 3025

x^2 = 5050

x = 5√202

5 0
3 years ago
What is the distance between the points (5.-18) and (8,
romanna [79]

Answer:

\sqrt{10}

Step-by-step explanation:

The horizontal distance from points (5,-18) and (8,-17) is 3 because it is 3 units from 5 to 8.  The vertical distance is 1 since it is one unit from -18 to -17.  Now we can use the equation a^{2}+b^{2}=c^{2} where a=3 and b=1 and c is the distance that you are looking for:

a^{2} +b^{2} =c^{2}\\3^{2} +1^{2} =c^{2}\\9+1=c^{2}\\10=c^{2}\\\sqrt{10}=c

8 0
2 years ago
Read 2 more answers
IL COSL al we creeree viall
kakasveta [241]

Answer:

<em>In the next year, Anthony worked 2,084 hours</em>

Step-by-step explanation:

Anthony worked 1,697 hours in 2010.

We also know Anthony worked 22.8% more hours than in 2010.

The problem requires to calculate how much did Anthony work in the next year.

It can be calculated as follows:

Take 22.8% of 1,697:

22.8 * 1,697 / 100 = 386.916\approx 387\ hours

Now calculate by adding it to the original number of hours:

1,697 + 387 = 2,084 hours

In the next year, Anthony worked 2,084 hours

8 0
3 years ago
Marsha is buying a new cell phone. She has a 45% off coupon from the store. She pays $275 for the cell phone. What is the price
jekas [21]

Answer:

The price of the cell phone without the coupon= $500

Step-by-step explanation:

Step 1: Express discounted amount

The discounted amount can be expressed as a function of the original  cost of the phone as follows;

D=r×A

where;

D=discounted amount

r=coupon rate

A=original price of the cell phone before the coupon

In our case;

r=45%=45/100=0.45

A=a

replacing;

Discounted amount=(0.45×a)=0.45 a

Step 2: Amount she pays up

Amount she pays=Original cost of cell phone-discounted amount

where;

Amount she pays= $275

original cost of cell phone=a

discounted amount=0.45 a

replacing;

$275=a-0.45 a

0.55 a=275

a=275/0.55

a=500

The price of the cell phone without the coupon= $500

7 0
3 years ago
A rotating wind turbine has a diameter of about 145 feet and its circumference is about 456 feet. A smaller model of the turbine
Serjik [45]

Answer:

ross-multiplication.

circumference divided by the diameter

10/x = 580/185

10x185=1850

1850/580=3.189

Step-by-step explanation:

give me brainliest

7 0
3 years ago
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