The projected T. rex is about 10 meters long by 4.6 m tall. If the actual image of the T. rex on the projector lens is only 2 centimeters tall, what is the scale factor for the projection?(Hint: Watch your units!)

230

Step-by-step explanation:

The scale factor is by what amount the bigger is bigger than smaller, or what amount the smaller is smaller than the bigger.

Now, we first have to use same units. Lets use cm.

We know 100 cm = 1 meter

For projection (big one):

10 meters by 4.6 meters, that, in cm would be:

10*100 = 1000 cm

4.6 * 100 = 460 cm

So, the projection is:

1000cm (long) by 460 cm (tall)

The T-Rex on lens is:

x cm (long) by 2 cm (tall)

So, the height is given for both, so we can see that

2cm in lens is to 460 cm in projector

The scale factor is:

460/2 = 230

That means the projected image is 230 times the real image

THe scale factor is 230

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 ☺