For an object whose velocity in ft/sec is given by v(t) = -3t2 + 5, what is its displacement, in feet, on the interval t = 0 to t = 2 secs?

Step-by-step explanation:

To find the displacement I'll give you two ways since I don't know if you had experience with calculus. So here's both ways.

Way 1: Graph 1: Geometric Apporoach.

I'll a graph where t is x axis and v is y axis. So we have a velocity versus time graph.

Then, we graph the function

Look Above this what graph I get

Now, to find displacement,

Remeber displacement is the product of velocity and time. So here displacement is area under the curve.

We want displacement from 0 to 2. so let form the shape under the curve.

Look at the second graph, we form a triangle and we get this

Area of Triangle is 1/2 bh.

The base is 2 and the height is -6 so we get

Our height is -12 because velocity is a vector so it can be negative and down is negative.

So the displacement is -12

Way 2: Calculus Way.

We can use integration to find the answer.

So now we have

Now we do,

So the area under the curve is -12. Thus displacement is -12

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720