Question

If a cube with side length 6 inches has its dimensions divided in half, what will be the volume of the new cube?

Answer 1

Cut 6 in half to get ???

Answer 2

now cube that

Answer 3

3^3 = 3*3*3 = ??

Answer 4

27

Answer 5

good

Answer 6

That's your answer since the volume is

V = s^3

where

V = volume
s = side length

Answer 7

yes its correct thank you..can u answer this? A fire truck has a ladder that can extend to 60 feet in length. The ladder can be safely raised to a maximum angle of 75° with the horizontal. Disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?

Answer 8

lets draw a pic first

Answer 9

if we do, we might get something like this

Answer 10

our goal is to find h

Answer 11

to tie h and 60 together (along with the angle 75 degrees), we use the sine function

this is because sine = opposite/hypotenuse where

opposite = h
hypotenuse = 60

Answer 12

so this means

sin(75) = h/60

Answer 13

solve for h, what do you get?

Answer 14

second sine? or just sine?

Answer 15

what do you mean by second sine

Answer 16

on the scientific calculator if u r finding the angle you have to press second then sin to find the correct answer

Answer 17

ah i see what you meant

Answer 18

but now i see that the angel is given

Answer 19

that's known as inverse sine or arcsine

Answer 20

angle*

Answer 21

if you have sin(x) = 1/2 for instance and you wanted to solve for x, you would apply the arcsine to both sides to get

x = arcsin(1/2)

Answer 22

to evaluate arcsin(1/2), you would type "2nd", "sin", "1", "/", "2", "enter"

Answer 23

makes sense

Answer 24

in our case, we don't need to use arcsine because we dont need to solve for the angle

so we just isolate h like this

sin(75) = h/60

60*sin(75) = h

h = 60*sin(75)

h = 60*0.9659258 ... use a calculator here (make sure you're in degree mode)

h = 57.955548

Answer 25

yay its correct

Answer 26

lol that's good

Answer 27

thank you

Answer 28

you're welcome