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

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.