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3 years ago

Attached pic...please simplify

Mathematics

2 answers:

liraira [26]3 years ago

5 0

Answer:

The answer is C

kati45 [8]3 years ago

3 0

Answer: C

Explanation:

First use the properties of radicals to get y / x * 1 / 2y.

Multiply the fractions to get y / x root 2y.

Next up rationalize and you get root 2y/2x

So your answer is C

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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

2 years ago

What is the value of x in the equation 1.5(x + 4) - 3=4.5(x-2)

anyanavicka [17]

Hi there!

The Eqn. is :-

1.5 (x + 4) - 3 = 4.5 (x - 2)

1.5x + 6 - 3 = 4.5x - 9

Combining the like terms :-

1.5x - 4.5x = - 9 - 6 + 3

- 3x = - 15 + 3

- 3x = - 12

x = $\dfrac {- 12}{- 3}$

x = 4

Hence, the required answer is → x = 4

~ Hope it helps!

8 0

3 years ago

Read 2 more answers

Find the mean and the standard deviation for each set of values. Show your work. 15,17,19,20,14,23,12

vekshin1

1. Mean.

$\overline{x}=\dfrac{15+17+19+20+14+23+12}{7}=\dfrac{120}{7}\approx\boxed{17.14}$

2. <span>Standard deviation.

First we have to square each value and calculate the mean of that squares:

$\overline{x^2}=\dfrac{15^2+17^2+19^2+20^2+14^2+23^2+12^2}{7}=\boxed{\dfrac{2144}{7}}$

so the variance:

$s^2=\overline{x^2}-\overline{x}^2=\dfrac{2144}{7}-\left(\dfrac{120}{7}\right)^2\approx\boxed{12.41}$

and the standard deviation:

$s=\sqrt{s^2}=\sqrt{12.41}\approx\boxed{3.52}$
</span>

3 0

3 years ago

Broccoli cost 1.50 per pound at the shop. How much money does 64 ounces of broccoli cost, before tax?

olga2289 [7]

The brocoli would cost 6 dollars.

8 0

3 years ago

Mother bake some cookies she get one set of the cookies

xz_007 [3.2K]

Answer:

She got one set.

4 0

3 years ago