Find the value of 2u+4 given -3u-1=2

Mathematics

1 answer:

eimsori [14]3 years ago

6 0

Answer: 2

Step-by-step explanation: Fist solve the first problem. -3u-1=2. That simplifies to -3u=3. Now divide each side by -3. Now you should have u=-1. Now put it in the other problem. 2(-1)+4. 2*-1 is -2. So -2+4=2

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3 years ago

Evaluate the sum of the following finite geometric series.

rjkz [21]

Answer:

$\large\boxed{\dfrac{156}{125}\approx1.2}$

Step-by-step explanation:

<h3>Method 1:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\\\\for\ n=1\\\\\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1\\\\for\ n=2\\\\\left(\dfrac{1}{5}\right)^{2-1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}\\\\for\ n=3\\\\\left(\dfrac{1}{5}\right)^{3-1}=\left(\dfrac{1}{5}\right)^2=\dfrac{1}{25}\\\\for\ n=4\\\\\left(\dfrac{1}{5}\right)^{4-1}=\left(\dfrac{1}{5}\right)^3=\dfrac{1}{125}$

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}=1+\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}=\dfrac{125}{125}+\dfrac{25}{125}+\dfrac{5}{125}+\dfrac{1}{125}=\dfrac{156}{125}$

<h3>Method 2:</h3>

$\sum\limits_{n=1}^4\left(\dfrac{1}{5}\right)^{n-1}\to a_n=\left(\dfrac{1}{5}\right)^{n-1}\\\\\text{The formula of a sum of terms of a geometric series:}\\\\S_n=a_1\cdot\dfrac{1-r^n}{1-r}\\\\r-\text{common ratio}\to r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=\left(\dfrac{1}{5}\right)^{n+1-1}=\left(\dfrac{1}{5}\right)^n\\\\r=\dfrac{\left(\frac{1}{5}\right)^n}{\left(\frac{1}{5}\right)^{n-1}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\r=\left(\dfrac{1}{5}\right)^{n-(n-1)}=\left(\dfrac{1}{5}\right)^{n-n+1}=\left(\dfrac{1}{5}\right)^1=\dfrac{1}{5}$

$a_1=\left(\dfrac{1}{5}\right)^{1-1}=\left(\dfrac{1}{5}\right)^0=1$

$\text{Substitute}\ a_1=1,\ n=4,\ r=\dfrac{1}{5}:\\\\S_4=1\cdot\dfrac{1-\left(\frac{1}{5}\right)^4}{1-\frac{1}{5}}=\dfrac{1-\frac{1}{625}}{\frac{4}{5}}=\dfrac{624}{625}\cdot\dfrac{5}{4}=\dfrac{156}{125}$

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4 years ago

Meg wants to find hie nany phones the company activated in one minute explain why meg can use 15000 divided by 50 to

Gemiola [76]

Answer:

300 phones the company activated in one minute

As per unitary method, calculation been done to find the value of single unit from the value of multiple units.

So, she is dividing the total number of phone activated by number of minutes taken to activate to find phone activate in one minute.

Step-by-step explanation:

Here is the correct question: Meg wants to find how many phones the company activated in one minute. Explain why meg can use 15000 divided by 50 to find the answer.

As per unitary method, calculation been done to find the value of single unit from the value of multiple units.

Therefore, in the above question Meg knew the number of total phone activated by company in 50 minutes, which is 15000.

Now, she want to find how many phones the company activates in one minute.

So, she is dividing the total number of phone activated by number of minutes taken to activate to find phone activate in one minute.

Phones the company activated in one minute= $15000\div 50= 300\ phones$