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4 years ago

What is an inverse statement

Mathematics

1 answer:

shusha [124]4 years ago

4 0

Answer:

1 | noun | a message that is stated or declared; a communication (oral or written) setting forth particulars or facts etc

2 | noun | a fact or assertion offered as evidence that something is true

3 | noun | (music) the presentation of a musical theme

4 | noun | a nonverbal message

5 | noun | the act of affirming or asserting or stating something

6 | noun | (computer science) a line of code written as part of a computer program

7 | noun | a document showing credits and debits

(7 meanings)

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

???????????????????????????????????????????????????????????????????????????????????????????????????????????????/

uranmaximum [27]

Answer: 10,000

Step-by-step explanation:

5 0

3 years ago

Purchase price of article = $5,555 Down payment = $555 Number of payments = 42 True annual interest rate=18% Monthly Payment= $

bixtya [17]

The answer to the monthly payment is $257.1428571 or $258.

How to get the answer:
Simply minus $5555 to $555. You get $5000.
Then, divide $5000 to the number of payments which is 42. (5000/42)
For that, you get a total of 119.047619. But that is not the final answer yet.
Next, we will multiply 119.047619 to 12, because we are looking for the monthly payment and we were given an "annual" rate. Annual means yearly and every year we have twelve (12) months. In that case, 119.047619 multiplied by 12 is equal to 1428.571428. Still, it is not the final answer.
The last step is, we will multiply the answer 1428.571428 to 18% or .18 and we get a total of 257.142857. Since we used the unit $ then we will a dollar for the answer. Completing the answer to the ]question, we get a total of $257.142857 or $258 for the monthly payment.

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3 years ago

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How to do a diagram in math for kelly correctly answered 80% of the 20 questions on the test

Dvinal [7]

Step-by-step explanation:

80:100=x:20

x=80×20/100=16

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Help me find the volume please

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