Which expression is equivalent? (5/7)x

What is the distance between the points (-4, 2) and (1, -3) on the coordinate plane?

ruslelena [56]

Answer:

A. 7.07 units

Step-by-step explanation:

Use the distance formula for coordinates:

$d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2 }$

Fill in the coordinates accordingly:

$d=\sqrt{(1-(-4))^2+(-3-2)^2}$

which simplifies down to

$d=\sqrt{25+25}$

which is of course

$d=\sqrt{50}$

Plug that into your calculator and you'll get the answer

4 0

3 years ago

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

Which value is equivalent to 3/11? OA A. 0.27 O B. 0.27 OC C. 3.6 OD. 3.

Sladkaya [172]

Answer:

0.27 repeating.

Step-by-step explanation:

So to solve this we just have to use division.

1 clearly doesnt go into 3 at least one time, so we can add a decimal point and add a 0 to make it 30.

11 goes into 30 2 times, so we have:

0.2

and 30-22=8

So we can add another 0 and make it 80.

Then 11 goes into 80 7 times. So we have:

0.27

and 80-77=3

So again, add the 0, we have 30.

11 goes into 30 2 times, so:

0.272

and 30-22=8

Add another 0 we get 80.

11 goes into 80 7 times.

So finally, we have:

0.2727.

This is a repeating decimal.

This can be shown as:

0.27

So this is your answer!

I was a bit confused with which one it was on your answer key, but knowing that it is 0.27 I am guessing you can chose!

Hope this helps!

4 0

2 years ago

What is the percent equivalent of 11.21? Select one: A. 112.1% B. 0.1121% C. 1,121% D. 11.21%

pogonyaev

It would be 11.21 percent, hope it helps.

5 0

3 years ago

What is the volume of the cylinder? Use 3.14 for . 4 cm 11 cm

Genrish500 [490]

Answer:

Use the formula,

Volume of cylinder =πr²h

=3.14×16×11

=552.64 cm³

3 0

2 years ago