The distance s (in m) above the ground for a projectile fired vertically upward with a velocity of 4[a] m/s as a function of time t (in s ) is given by s=4[a]t−4.[b]t2..

a=3, b=7

find latex: t for latex: v=0, find find latex: v for latex: t=4, find find latex: v for latex: t=5. what conclusions can you draw?

find the answers to these questions. what conclusions can you draw?

Answers:

a) 1.224 s

b) -27.2 m/s

c) -37 m/s

Step-by-step explanation:

According to the given information the distance is given by:

(1)

In additio, since the projectile was fired vertically we can use the following equation:

(2)

Where:

is the final velocity

is the initial velocity

is the acceleration due gravity

is the time

Knowing this, let's begin:

a) Find  for

Using (2):

(3)

(4)

(5)

(6)

b) Find for

In this case we have to find :

(7)

(8)

c) Find for

(9)

(10)

Conclusions:

The time we found in a) when is at the maximum height of the projectile, just before going down. That is why in parts b) and c) when time is and the velocity is negative, because it is directed downwards.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: