Terry is filling spherical water balloons with a faucet that puts out 100 cm 3 100 cm 3 100, start text, space, c, m, end text, cubed of water per second. At that rate, it takes Terry 6 66 seconds to fill a balloon. What is the radius of a filled balloon?

Correct question is;

Terry is filling spherical water balloons with a faucet that puts out 100 cm³ of water per second. At that rate, it takes Terry 6 seconds to fill a balloon. What is the radius of a filled balloon?

r = 5 cm

Step-by-step explanation:

Volume of a sphere is;

V = (4/3)πr³

It takes 6 seconds to fill the balloon when a faucet that puts out 100 cm³ of water per second.

Thus,

Volume of balloon = 100 × 6 = 600 cm³

Thus;

(4/3)πr³ = 600

r³ = (600 × 3)/4π

r³ = 143.239

r = ∛143.239

r = 5.23

Approximation to the nearest whole number gives; r = 5 cm

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.