A ball is thrown into the air with a velocity of 35 ft/s. Its height, in feet, after t seconds is given by s(t) = 35t − 16t2.
Find the velocity (in ft/s) of the ball at time
t = 1 second.

Answer explained below

Step-by-step explanation:

the equation of motion when an object is accelerated is given by:

where

x - is the current position(or displacement) of the body

x0 is the initial position

v0 is the initial velocity

a is acceleration

t is time

We rewrite the equation

which is similar to the equation above, which means we can rewrite the following equation like this:

so, in our case:

x0 = 0

v0 = 35 m/s

Now, since this is an accelerated motion it means that the velocity of the body changes as well due to acceleration with the equation:

acceleration is negative, therefore:

t = 1 results:

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:

c. 6tan80

step-by-step explanation: