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valentinak56 [21]

2 years ago

8

4.2 y minus 5.2 = 18.5

1 answer:

Levart [38]2 years ago

5 0

Step-by-step explanation:

4.2y=23.7

y=5.642857

YAYYYYYYYYYYYYYYYYYYY

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3 years ago

Read 2 more answers

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

2 years ago

What is the value of x in the equation 4x+8y=40, when y=0.8?

lubasha [3.4K]

4x+8y=40
0.8*8=6.4
4x+6.4=40
40-6.4=33.6
4x=33.6
33.6\4=8.4
X=8.4

6 0

3 years ago

Triangle- interior angle<br> Please help !

sp2606 [1]

Answer:

x = 25

<B = 120 degrees

<C = 30 degrees

Step-by-step explanation:

Total angle measure of a triangle - 180 degrees

Add all the angles together to find the value of x

30 + 4x + 20 + x + 5 = 180

55 + 5x = 180

55 - 55 + 5x = 180 - 55

5x = 125

$\frac{5x}{5} = \frac{125}{5}$

x = 25

<B = 4(25) + 20

<B = 100 + 20

<B = 120

<C = 25 + 5

<C = 30

7 0

3 years ago