# 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.

https://brainmass.com/math/algebra/algebra-geometry-problems-557771

#### 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.