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3 years ago

How to write numbers in two other forms ? 6,007,200

1 answer:

5 0

<span>in words: six million, seven thousand two hundred or in scientific notation: 6.0072 x 106in expanded form: 6 000 000 + 0 + 0 + 7000 + 200 + 0 + 0</span>

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I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

8 0

1 year ago

Trey evaluated 12/15 + 1/10 and got an answer of 13

bija089 [108]

Answer:

C. His answer is correct because 12 + 1 = 13 and 15 + 10 = 25.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

-4x+5 + -13x+39=180 angle measure

mylen [45]

Step-by-step explanation:

−4x+5−13x+39=180

Step 1: Simplify both sides of the equation.

−4x+5−13x+39=180

−4x+5+−13x+39=180

(−4x+−13x)+(5+39)=180(Combine Like Terms)

−17x+44=180

Step 2: Subtract 44 from both sides.

−17x+44−44=180−44

−17x=136

Step 3: Divide both sides by -17.−17x

−17

136

−17

x=−8

Answer:

x=−8

5 0

2 years ago

Write your answer with no spaces and any fraction with “/“

Archy [21]

Answer:

The slope is 1/2

Step-by-step explanation:

Hi!

Disclaimer: Just for this response, I'm going to write it the same way you write a fraction out on paper just so it's easier to see.

First, you plot the two coordinates on the graph:

(0,0) and (2,1)

The formula for slope is $\frac{y1 - y2}{x1 - x2}$

Now we plug in numbers accordingly:

$\frac{0 - 1}{0 - 2}$

Simplify:

$\frac{-1}{-2} \\$

Simplify:

$\frac{1}{2}$

Let me know if you have any questions

6 0

2 years ago

Based on the model, approximately how many customers will be on the restaurant when there are 10 cars parked in the restaurant’s

Zanzabum

Answer:

Step-by-step explanation:

From the graph, derive the best fit equation :

Using the points ;

(0,2.5) (100 ,35)

x1 = 0 ; y1 = 2.5 ; x2 = 100 ; y2 = 35

Slope formula, m = (y2-y1)/(x2-x1)

m = (35-2.5)/(100-0)

m= (32.5)/100

m = 0.325

The y intercept, value on the graph where best fit line crosses the y axis = 2.5

The equation :

y = mx + c

c = intercept ; m = slope

y = 0.325x + 2.5

y = Number of cars

x = number of customers

The number of customers if there are 10 cars parked :

10 = 0.325x + 2.5

10 - 2.5 = 0.325x

7.5 = 0.325x

x = 7.5 / 0.325

x = 23.076

x = 23

6 0

3 years ago