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3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Mathematics

1 answer:

hichkok12 [17]3 years ago

7 0

Answer: -129

Step-by-step explanation:

Given the sequence {-3, 6, -12, 24, ... }, we can see that the first term (a) is -3 and the ratio (r) is $\dfrac{6}{-3} = -2$ .

Input those values into the Sum formula:

$S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_7=\dfrac{-3(1-(-2)^7)}{1-(-2)}\\\\.\quad=\dfrac{-3(1-(-128))}{1+2}\\\\.\quad=\dfrac{-3(1+128)}{3}\\\\.\quad=\dfrac{-3(129)}{3}\\\\.\quad=-129$

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Answer:

The value of x component changes at a rate of $\frac{dx}{dt}=4\sqrt{x}$ units per second

Step-by-step explanation:

We are given that $y=x^{\frac{1}{2}}$

Differentiating on both sides with respect to time we get

$\frac{dy}{dt}=\frac{d\sqrt{x}}{dt}\\\\\frac{dy}{dt}=\frac{1}{2}x^{\frac{-1}{2}}(\frac{dx}{dt})\\\\\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}$

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To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
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To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

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$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
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The triangular matrix looks like:

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