Jack can swim 12 laps in 28 minutes. 28 minutes is 4 times greater than the time it took him to swim 3 laps. With 28 minutes he should therefore be able to swim 4 times as many laps. 3 times 4 equals 12
Answer:
Please check the explanation.
Step-by-step explanation:
Given the vector
v = 6i + 2√3j
The Magnitude of a vector:
![\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}](https://tex.z-dn.net/?f=%5Cmathrm%7BComputing%5C%3Athe%5C%3AEuclidean%5C%3ALength%5C%3Aof%5C%3Aa%5C%3Avector%7D%3A%5Cquad%20%5Cleft%7C%5Cleft%28x_1%5C%3A%2C%5C%3A%5C%3A%5Cldots%20%5C%3A%2C%5C%3A%5C%3Ax_n%5Cright%29%5Cright%7C%3D%5Csqrt%7B%5Csum%20_%7Bi%3D1%7D%5En%5Cleft%7Cx_i%5Cright%7C%5E2%7D)
![=\sqrt{6^2+\left(2\sqrt{3}\right)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B6%5E2%2B%5Cleft%282%5Csqrt%7B3%7D%5Cright%29%5E2%7D)
![=\sqrt{36+12}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B36%2B12%7D)
![=\sqrt{48}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B48%7D)
![\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D)
![=\sqrt{3}\sqrt{2^4}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B3%7D%5Csqrt%7B2%5E4%7D)
![=4\sqrt{3}](https://tex.z-dn.net/?f=%3D4%5Csqrt%7B3%7D)
The Direction of a vector:
tan Ф = y/x
y=2√3
x = 6
tan Ф = y/x
= 2√3 / 6
= √3 / 3
![\theta \:=tan\:^{-1}\left(\frac{\sqrt{3}}{3}\right)](https://tex.z-dn.net/?f=%5Ctheta%20%5C%3A%3Dtan%5C%3A%5E%7B-1%7D%5Cleft%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D%5Cright%29)
![\:\theta \:=\frac{\pi \:}{6}=30^{\circ \:}](https://tex.z-dn.net/?f=%5C%3A%5Ctheta%20%5C%3A%3D%5Cfrac%7B%5Cpi%20%5C%3A%7D%7B6%7D%3D30%5E%7B%5Ccirc%20%5C%3A%7D)
Answer:
pi times 4
Step-by-step explanation:
Circumference: pi times diameter (pi)(d) or pi times 2 times the radius (pi)(2r)
A chemical process by which autotrophs prepare there own food is called photosynthesis