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I will use i j k notation for presentation.

Magnitude of the vector a = 6i+4j

\(||\mathbf{a}||\\ =\sqrt{6^2+4^2}\\ =\sqrt{36+16}\\ =\sqrt{52}\\ =2\sqrt{13}\)

I have just learnt what's vectors 2 days ago :D

Yea of course!!

x + 2y = 7

2x + 3y = 11

This system have exactly 2 solutions, namely x=1 and y=3.

e^(2x) ? 8e^(x) + 7 = 0 solve for x

Find the Cartesian equivalent to the parametric equation x(t)= 3-2t and y(t)=(t^2) -2t

\(\begin{array}{|rcll|} \hline x(t)&=& 3-2t \\ x-3 &=& 2t \\ \mathbf{2t} &\mathbf{=}& \mathbf{ x-3 }\\ \mathbf{t} &\mathbf{=}& \mathbf{\frac12 (x-3) } \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline y(t)&=&(t^2) -2t \qquad &| \qquad \mathbf{t =\frac12 (x-3) } \\ y &=&[ \frac12 (x-3) ]^2 -(2t) \qquad &| \qquad \mathbf{2t = x-3 }\\ y &=&[ \frac12 (x-3) ]^2 -(x-3) \\ y &=&\frac14 (x-3)^2 -(x-3) \\ y &=&\frac14 (x-3)^2 -(x-3)\cdot \frac44 \\ y &=&\frac14 (x-3)\cdot [(x-3)-4] \\ y &=&\frac14 (x-3)\cdot [ x-3 -4] \\ y &=&\frac14 (x-3)\cdot ( x-7 ) \\ y &=&\frac14 (x^2-7x-3x+21) \\ \mathbf{y} &\mathbf{=}&\mathbf{ \frac14 \cdot (x^2-10x+21) }\\ \hline \end{array}\)

I assume that the function is  

f(x)  = l x  l   - 1

And we wantt o evaluate

f(-2)  =  l -2 l   - 1    =       2  - 1    =     1

It is a function of x because it passes the "Vertical Line Test."  However, the domain is restricted to [-4, infinity )

Here's the graph:  https://www.desmos.com/calculator/lpvemajllx

Area = Length * Width

300 =  Length * 20       divide both sides by 20

15 = Length  [in cm]

Let the point  be  (1, -4)  = (x1, y1)

And in the point-slope form we have :

y - y1  = m ( x - x1)    substituting, we have

y - (-4)  = (2/3) (x - 1)      

y + 4  = (2/3) (x - 1)     and so forth

Another way to chack that my answer is correct is to sub 1 into the final equation......so we have

y = (2/3)(1)  - 14/3

y = 2/3 - 14/3

y = -12/3   = -4      which   gives us the point (1, -4)

Let's look at this in a slightly different manner. Orient the box so that the base is 8 x 6 and the height is 18.

For the bottom layer, and top layers, 48 cubes are touching the box in each layer.

For the other 16 layers, 48 - 16 - 8 = 24 cubes are NOT touching the box in each layer.

So.......the number of cubes rouching the box must be the total cubes less the number that are not touching the box =

864 - 16(24)  = 480 cubes touch the box

Another way to see this is that 96 cubes in total touch the top and bottom layers. And for each of the other 16 layers, as many cubes in each layer touch the box as the ones that don't

So  96 + 16(24)   = 480 cubes touch the box

@CPhill... where did the y-(-4) come from tho....

Let's say you had something like 0.4 * 0.67. You could think of 0.4 as 4/10, and 0.67 as 67/100. Then, just multiply 4*67: 4*60 = 240, + 4*7=28 --> 240 + 28 = 268. Then, multiply the denominators: 1/10 * 1/100 = 1/1000. Combine the two to get 268/1000 = 0.268. 

Hope this helps.

Take it from here

y - (-4)  = (2/3)(x - 1)   simplify

y + 4  = (2/3)x - 2/3      subtract 4 from both sides

y = (2/3)x - 2/3 - 4

y = (2/3)x - (4 + 2/3)

y = (2/3)x - 14/3

You can just use algebra to rearrange the terms into the y=mx+b form.

y - 4 = 2/3(x - 1)

                  ^ distribute   

-> y - 4 = 2x/3 -2/3

       +4             +4= 12/3

-> y = 2x/3 + 10/3

Think about an 8*16*8 rectangular prism (made of 1*1*1 sugar cubes) that is empty on the interior. This is all the sugar cubes that are touching the box. To 'empty' the box, you would have to subtract a box slightly smaller in dimensions. Subtracting 2 from each dimension, you get a 6*14*6 box that would fit inside of the 8*16*8 box. (8*16*8)-(6*14*6) = 520 sugar cubes that are touching the box.

-3-x=-(x+5)+3   simplify the right side

-3 - x   =  -x - 5 + 3

-3 - x   = -x - 2   add x to both sides

-3   =  -2     and this is never true.....so.....this has no solution

[9 + 9] - [9/9] =

18    -      1    = 17

Divide volume by the base area.

Thank you

7/6 as a decimal is pretty much 7 divided by 6. so it would be 1.16 repeating. :)