SOLUTION: 1) Explain an advantage of rational exponents over the radical sign 2) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your star

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: 1) Explain an advantage of rational exponents over the radical sign 2) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your star      Log On


   

Question 72726: 1) Explain an advantage of rational exponents over the radical sign
2) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively. Round to the tenth's place
3)The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 729 cm3.


Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
1) One advantage is when multiplying. For example:
sqrt%283%29sqrt%283%29 This is easier to understand when written this way: 3%5E%281%2F2%29+%2A+3%5E%281%2F2%29+=+3%5E%28%28%281%2F2%29%2B%281%2F2%29%29%29 = 3%5E1+=+3
2) For this problem, use the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2
a=35 km and b = 65 km. Let d = the unknown distance.
d%5E2+=+35%5E2%2B65%5E2 Simplify.
d%5E2+=+1225%2B4225
d%5E2+=+5450 Take the square root of both sides.
d+=+sqrt%285450%29
d+=+73.824
d+=+73.8km. (Rounded to the nearest tenth)
3) V+=+s%5E3 To find s, take the cube root of both sides.
729+=+s%5E3 Take the cube root.
9+=+s The length of the side is 9 cm.