The velocity of a moving object, v, in meters per second, is given by the formula below. the variable is the kinetic energy of the object, in joules, and m is the mass of the object, in kilograms. a marble with a mass of 0.04 kilograms rolls down a ramp and reaches a maximum kinetic energy of 0.875 joules. use the given formula to write a function, v(x)c that models the situation. then use the function to predict how the velocity of the marble changes as it rolls down the ramp

Option B: As the kinetic energy increases, velocity increases until it reached the maximum kinetic energy.

Explanation:

From law of conservation of energy, total energy of a closed system remains constant. One form of energy can convert to another.

Here, when a marble is kept on the ramp, it would have energy = potential energy. On reaching the bottom of the ramp, all the potential energy would be converted to kinetic energy (maximum). In between, it would have both potential as well as kinetic energy.

Potential energy at any given point on ramp, = mg x where x is the height of the marble which varies as marble rolls down the ramp.

So, as the kinetic energy increases, the velocity increases until it reaches the maximum kinetic energy. correct option is B.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: