How do you write 4/25 as a decimal

Mathematics

1 answer:

Helga [31]3 years ago

3 0

.16 because 4 divided by 25 it .16

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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

Wendell is curious how much space Jordan will have inside the doghouse to move around in. What is the volume of the

Luda [366]

Answer:

24,840 cubic inches

Step-by-step explanation:

18 x 30 = 540 - rectangle house front surface area

540 + .5(30 x 10) = 690 - triangle house front surface area

690 x 36 = 24,840 - (rectangle + triangle surface area) x depth

7 0

3 years ago

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A vegetable garden with an area of 200 square feet is to be fertilized. If the length of the garden is 1 foot less than three ti

charle [14.2K]

Ok so I like to go in steps with these questions- first draw a picture and identify your variables.

W=width
L= 3w-1

Now we know that length times width gets us area so we plug in our variables into the area equation.

200 = w(3w-1)

When you foil that equation you end up with a quadratic : 3w^2-w-200 = 0

Either factor that or use the quadratic formula to get
w= 8.33 and w= -8

Since you can't have a negative dimension you need to use 8.33 and plug it back into your length equation.

Final answer:

w= 8.33ft
l= 23.99ft

*Now I simplified the decimals a little bit so you end up with 199.8ft^2 for the area so just add a few decimals on here and there*

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3 years ago

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Simplify (5x - 7y) - ( x + 3y)

ruslelena [56]