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3 years ago

Simplify i^38 1) i 2) -1 3) -i 4) 1

Mathematics

2 answers:

alexdok [17]3 years ago

7 0

The awnser is supposed to be -1

Nataly_w [17]3 years ago

5 0

the answer is number 2.

$- 1$

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Y=4x+8forx <br> Thank you if you can answer

yKpoI14uk [10]

Answer:

y=4x-8. y=4x−8 y = 4 x -

Step-by-step explanation:

I think is it

7 0

2 years ago

Read 2 more answers

The next number in the arithmetic sequence 10,23,36,? Is

rjkz [21]

It would be 49
10+13=23
23+13=36
36+13=49
I think this is right

6 0

3 years ago

Determine if the columns of the matrix form a linearly independent set. Justify your answer. [Start 3 By 4 Matrix 1st Row 1st Co

Volgvan

Answer:

Linearly Dependent for not all scalars are null.

Step-by-step explanation:

Hi there!

1)When we have vectors like $v_{1},v_{2},v_{3}, ...$ we call them linearly dependent if we have scalars $a_{1},a_{2},a_{3},...$ as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.

$a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...a_{m}\vec{v_{m}}=0$

When all scalar coefficients are equal to zero, we can call them linearly independent

2) Now let's examine the Matrix given:

$\begin{bmatrix}1 &-2 &2 &3 \\ -2 & 4 & -4 &3 \\ 0&1 &-1 & 4\end{bmatrix}$

So each column of this Matrix is a vector. So we can write them as:

$\vec{v_{1}}=\left \langle 1,-2,1 \right \rangle,\vec{v_{2}}=\left \langle -2,4,-1 \right \rangle,\vec{v_{3}}=\left \langle 2,-4,4 \right \rangle\vec{v_{4}}=\left \langle 3,3,4 \right \rangle$ Or

Now let's rewrite it as a system of equations:

$a_{1}\begin{bmatrix}1\\ -2\\ 0\end{bmatrix}+a_{2}\begin{bmatrix}-2\\ 4\\ 1\end{bmatrix}+a_{3}\begin{bmatrix}2\\ -4\\ -1\end{bmatrix}+a_{4}\begin{bmatrix}3\\ 3\\ 4\end{bmatrix}=\begin{bmatrix}0\\ 0\\ 0\end{bmatrix}$

2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.

Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.

$\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ -2 &4 &-4 &3 \\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )R_{1}\times2 +R_{2}\rightarrow R_{2}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &0 &9 &0\\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\ R_{2}\Leftrightarrow R_{3}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &1 &-1 &4 \\ 0 &0 &9 &0 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )$ $\left\{\begin{matrix}1a_{1} &-2a_{2} &+2a_{3} &+3a_{4} &=0 \\ &1a_{2} &-1a_{3} &+4a_{4} &=0 \\ & & &9a_{4} &=0 \end{matrix}\right.\Rightarrow a_{1}=0, a_{2}=a_{3},a_{4}=0$

$S=\begin{bmatrix}0\\ a_{3}\\ a_{3}\\ 0\end{bmatrix}$

3 0

3 years ago

A salesman who makes $32,500 a year gets promoted to sales manager, earning a new salary of $43,250. What was the rate of increa

OLEGan [10]

Answer:

33.1%

Step-by-step explanation:

First, calculate the dollar amount of the increase. Subtract $32,500 from $43,250. We get $10,750.

Next, divide this $10,750 by the original salary, $32,500, to determine what fraction of $32,500 is represented by $10,750:

fraction = $10,750/$32.500 = 0.331

Convert this to a percentage by multiplication by 100%: 33.1%

The rate of increase of the saleperson's salary was 33.1%.

8 0

2 years ago

A bag of chocolate mix weighed 1/4 of a kilogram could make enough brownies to feed 1/7 of the students at school how many bags

Hoochie [10]

A "whole" will be 7/7, or just 1 whole.

so we know one bag can do 1/7 of all students, how many will it be needed to do 7/7?

well, in 7/7 there are seven 7/7, so, 7 bags then, or one could say,

$\bf \begin{array}{ccll}
\stackrel{chocolate}{bag}&\stackrel{fraction}{students}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&\frac{1}{7}\\\\
x&\frac{7}{7}
\end{array}\implies \cfrac{1}{x}=\cfrac{\quad \frac{1}{7}\quad }{\frac{7}{7}}\implies \cfrac{1}{x}=\cfrac{1}{7}\cdot \cfrac{7}{7}
\\\\\\
\cfrac{1}{x}=\cfrac{1}{7}\implies 7=x$

5 0

2 years ago