A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.

Total time taken to inflate 2/3 balloon = 18.33 min

Step-by-step explanation:

Given:

Diameter = 55 ft

Radius r = 55 / 2 ft = 27.5

Rate of increase radius = 1.5 ft

Find:

Total time taken to inflate 2/3 balloon

Computation:

2/3 volume = [2/3][4/3]πr³

2/3 volume = [2/3][4/3][3.14][27.5]³

2/3 volume = 58,046.3889 (Approx)

2/3 volume = [2/3][4/3]πR³

58,046.3889 = [2/3][4/3][3.14]R³

20,796.875 = R³

R = 27.5 ft

Total time taken to inflate 2/3 balloon = 27.5 / 1.5

Total time taken to inflate 2/3 balloon = 18.33 min

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1