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Algebra, geometry problems

Check attachment for cleaner version of the questions below.

Solve the following equations algebraically. Must show work.
1a)
(t^{frac{2}{3}})
=4

b)√(5&x) + 1 = 3
= 3
c) =2-
(frac{2}{3})
(frac{5x -3}{x-1})
2)Solve algebraicaly
a)
(sqrt{x+2}-x=0)
b)
(4- frac{x}{x-2} = frac{-2}{x-2})
The volume of a cube is given by
( V = s^{3})
Find the length of a side of a cube ( round the answer to three decimal places if the volume is
(800_{cm}^{}3)
B)
(500^{cm}3)
4) The formula to find the wind chill temperature is given by
(w = 33- frac{10.45 + 10sqrt{v} - v)(33-T )}{22})
. V is wind speed in m/sec. Find the Wind Chill temperature given the following :
A ) T = 10 degree C , V= 9m/sec
B ) T = 0 degree C , V = 15 m/sec
C) T = -10 degree C , V = 20m/sec.

Attachments

Solution Preview

1.a.
t^(2/3) = 6
=> t = 6^(3/2) = (t^3)^(1/2) = 216^(1/2) == sqrt(216) = 14.70

1.b.
x^(1/5) + 1 = 3
=> x^(1/5) = 2
=> x = 2^5 = 32

1.c
(2/3) = 2 - (5x - 3)/(x-1)
=> (5x-3)/(x-1) = 2 - 2/3 = 4/3
=> 3*(5x-3) = 4*(x-1)
=> 15x - 9 = 4x - 4
=> 15x - 4x = 9 - 4
=> 11x = 5
=> x = ...

Solution Summary

Four algebra and geometry problems are solved.

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