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3 years ago

What is the solution to 12x = 72x -192

Mathematics

1 answer:

telo118 [61]3 years ago

8 0

Answer:

x = 3.2

Step-by-step explanation:

12x = 72x - 192

Add 192 to both sides of the equation

12x + 192 = 72x

Subtract 12x from both sides of the equation

192 = 60x

x = 3.2

Hope this helps :)

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3 years ago

Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

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3 years ago

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777dan777 [17]

Answer:

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Step-by-step explanation:

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2 years ago

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Dafna1 [17]

Answer:
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Explanation:
In case of multiplication of numbers with same base, we add the powers.
This means that:
a^x * a^y = a^(x+y)

Applying this to the given, we will find that:
(5^-1) * (5^-3) = 5^(-1-3)
= 5^-4
= 1/625

Hope this helps :)

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3 years ago

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