Answer:
its 400
Step-by-step explanation:
Answer:
![6\sqrt{3}i-6j](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7Di-6j)
Step-by-step explanation:
Given:
The magnitude, v=12
The angle
it makes with the positive x-axis =![150^0](https://tex.z-dn.net/?f=150%5E0)
Now for a vector (x,y)
; and
Therefore:
![150 =tan^{-1}(\frac{y}{x} )\\\frac{y}{x} =tan 150\\\frac{y}{x}=-\frac{\sqrt{3} }{3}](https://tex.z-dn.net/?f=150%20%3Dtan%5E%7B-1%7D%28%5Cfrac%7By%7D%7Bx%7D%20%29%5C%5C%5Cfrac%7By%7D%7Bx%7D%20%3Dtan%20150%5C%5C%5Cfrac%7By%7D%7Bx%7D%3D-%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D)
![y=-\frac{x \sqrt{3}}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7Bx%20%5Csqrt%7B3%7D%7D%7B3%7D)
Similarly:
![v=\sqrt{x^2+y^2}\\12=\sqrt{x^2+y^2}\\12^2=x^2+y^2\\144=x^2+y^2](https://tex.z-dn.net/?f=v%3D%5Csqrt%7Bx%5E2%2By%5E2%7D%5C%5C12%3D%5Csqrt%7Bx%5E2%2By%5E2%7D%5C%5C12%5E2%3Dx%5E2%2By%5E2%5C%5C144%3Dx%5E2%2By%5E2)
![144=x^2+(-\frac{x \sqrt{3}}{3} )^2\\144=x^2+\frac{3x^2}{9} \\144=\frac{4x^2}{3}\\4x^2=144 X 3=432\\x^2=108\\x=6\sqrt{3}](https://tex.z-dn.net/?f=144%3Dx%5E2%2B%28-%5Cfrac%7Bx%20%5Csqrt%7B3%7D%7D%7B3%7D%20%29%5E2%5C%5C144%3Dx%5E2%2B%5Cfrac%7B3x%5E2%7D%7B9%7D%20%5C%5C144%3D%5Cfrac%7B4x%5E2%7D%7B3%7D%5C%5C4x%5E2%3D144%20X%203%3D432%5C%5Cx%5E2%3D108%5C%5Cx%3D6%5Csqrt%7B3%7D)
Recall that:
![y=-\frac{x \sqrt{3}}{3}\\y=-\frac{6\sqrt{3} \sqrt{3}}{3}=-6](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7Bx%20%5Csqrt%7B3%7D%7D%7B3%7D%5C%5Cy%3D-%5Cfrac%7B6%5Csqrt%7B3%7D%20%20%5Csqrt%7B3%7D%7D%7B3%7D%3D-6)
Therefore: ![(x,y)=(6\sqrt{3}, -6)](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%286%5Csqrt%7B3%7D%2C%20-6%29)
The vector in the form ai+bj is therefore:
![6\sqrt{3}i-6j](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7Di-6j)
Answer:
Area is: 1,728 inches
Perimeter is: 168 inches
Step-by-step explanation:
Area= Length times width
Perimeter= length plus length plus width plus width.
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