Physics, 27.02.2020 00:33 thao5160

If the diameter of each of a car's wheels is 0.4 meters, approximately, what was the average speed of the car for its three-hour trip in which each wheel made 100,000 revolutions?

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Answer from: tonimgreen17p6vqjq

42 km/h was the average speed of the car for its three-hour trip.

Explanation:

Diameter of the car wheel = d = 0.4 m

Radius of the car wheel = r = 0.5 d = 0.5 × 0.4 m =0.2 m

Distance covered in 1 complete revolution = $2\pi r$

Distance covered in 100,000 complete revolution,D = $2\pi r\times 100,000$

$D=2\times 3.14\times 0.2 m\times 100,000=125,663.71 m$

1 m = 0.001 km

125,663.71 m = 125,663.71 × 0.001 km = 125.66371 km

Time taken to complete 100,000 revolution by a wheel = t = 3 hours

Speed of car : S

$S=\frac{125.66371 km}{3hours}=41.89 km/h\approx 42 km/h$

42 km/h was the average speed of the car for its three-hour trip.

Answer from: Quest

we have been given a quadratic function $f(x)=(x-5)^{2} +2$ and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is $[2,\infty)$ .

if we restrict the domain of this function to either $(-\infty,5]$ or $[5,\infty)$ , it will become one to one function.

let us know find its inverse.

$y=(x-5)^{2}+2$

upon interchanging x and y, we get:

$x=(y-5)^{2}+2$

let us now solve this function for y.

$(y-5)^{2}=x-2\\ y-5=\pm \sqrt{x-2}\\ y=5\pm \sqrt{x-2}\\$

hence, the inverse function would be $f^{-1}(x)=5+\sqrt{x-2}$ if we restrict the domain of original function to $[5,\infty)$ and the inverse function would be $f^{-1}(x)=5-\sqrt{x-2}$ if we restrict the domain to $(-\infty,5]$ .

Answer from: Quest

chemical energy --> gravitational potential energy --> kinetic energy --> elastic potential energy --> gravitational potential energy

explanation:

when emma starts the hike, the chemical energy stored in her body is used to climb up the mountain, and so she gains gravitational potential energy (because at the end, she will be at a higher height h above the ground). then she goes bungee jumping: as she falls, this gravitational potential energy is converted into kinetic energy (because her speed increases as she falls down), until the point when the rope stretches, and she stops moving. at that moment, all the kinetic energy is converted into elastic potential energy due to the stretching of the rope. then, this energy is released because the rope returns to its natural length, and emma gains a small increase in altitude $\delta h$ , so she gains some gravitational potential energy.

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If the diameter of each of a car's wheels is 0.4 meters, approximately, what was the average speed o...