Question

All objects have mass. Mass is the amount of material in an object, usually measured by its weight. Earlier in this unit, you studied the volume of objects. When you combine these two concepts, you get a useful measurement called density. The density of an object is its mass per unit of volume. Imagine two objects in which the larger one actually weighs less than the smaller one. This difference in weight is attributed to density.

Consider a candle that has a volume of 96 cubic inches and a weight of 44.16 ounces. What is the density of the candle? The density is defined as its mass per unit volume, so simply divide the mass of the candle by its volume:

.

In this case, you are finding the average density of the candle. In most cases, you will be finding the average density of objects because most objects do not have a uniform density. For instance, the portion of the candle where the wick is might have a different density than the rest of the candle.

Now that you know about density, let’s work on some applications.

Harold is a woodworker and is interested in finding the density of two different types of wood. He bought a pine log that has a 5-inch radius and is 30 inches long. The weight of the log is approximately 42.63 pounds. He also has an oak board that is 5.5 inches wide, 1.5 inches thick and 3 feet long. The board weighs approximately 8.05 pounds.
Part A
Which shapes can you use to model the log and the board?

Answer 1

@Vocaloid can u help me

Answer 2

@Hero can u help me wth this

Answer 3

so for the first part you're given 44.16 oz and 96 cubic inches, and asked to find density which is mass/volume

ounces (oz) are actually a measure of weight not mass, so unless the problem specifies oz/cm^3 as your units I would first convert oz to grams by multiplying

44.16 oz * 28.3495g/oz to get 1251.91392g
then divide that by the volume 96 cubic inches

Answer 4

so what do I put for the shaps

Answer 5

well what shape can you use to approximate a log? cube, cone, cylinder, prism?
what shape can you use to approximate a block of wood?

Answer 6

tbh idek

Answer 7

so a log of wood has two circular bases and a smooth side, with no edges, what shape is this?

Answer 8

cylinder

Answer 9

good, what about the block of wood? 6 flat sides and all 90 degree angles

Answer 10

idk

Answer 11

okay so the shapes i use is a rectangular prism and a cylinder

Answer 12

yes

Answer 13

k thx

Answer 14

If the endpoints AB of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB ?

Answer 15

okay

Answer 16

5, 3)




(4, 5)




(5, 5)




(4, 3)

that is the answer choices

Answer 17

basically, take the x-coordinates, add them together, divide by 2

then take the y-coordinates, add them together, divide by 2

then write them as a new set of coordinates (x,y)

Answer 18

i got (4,3)

Answer 19

is that right

Answer 20

good that's your answer

Answer 21

The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of CD is (-3 -1/3 1/3 3) . The possible coordinates of point D are {(4, 5) (5, 5) (6, 5) (8, 3)}and {(2, 1) (4, -1) (5, -1) (6, -1)} .

Answer 22

@Vocaloid

Answer 23

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD , and point C lies on AB . The length of is\[\sqrt{10}\] units.

Answer 24

well let's start by finding the slope of AB, let's use the slope formula:

Answer 25

A(2, 3) and B(8, 1)

therefore x1 = 2, x2 = 8 (the x-coordinates)
and y1 = 3 and y2 = 1 (the y-coordinates)

plug these in and find m

Answer 26

huh u lost me

Answer 27

okay

Answer 28

notice how x1 corresponds with 2, y1 corresponds with 3, etc.? so plug the values of y2, y1, etc. into the formula for m to find the slope

Answer 29

m=6/-2 right

Answer 30

I think you might have switched up your numerator and denominator

(1-3)/(8-2) = ?

Answer 31

yea so it would be -2/6

Answer 32

don't worry bout i guess my answer

Answer 33

good, that simplifies to -1/3

now we take the opposite reciprocal to get the slope of AB since its perpendicular, first we flip the num and denom of -1/3 to get -3, then we multiply by -1 to get ~3~ as the slope of CD

Answer 34

ok, so we have the slope of AB (-1/3 as we calculated earlier)

y = (-1/3)x + b

if we take the point (2,3) and plug these values in for x and y we get

3 = (-1/3)(2)+b

can you try solving for b?

Answer 35

anyway I really can't be here all day,

3 = (-1/3)(2) + b

subtract (-1/3)(2) from both sides

3 + (1/3)(2) = b

so b = 1/3

making the equation of CD

y = 3x + 11/3

you are given these possibilities for the points of C and C

{(4, 5) (5, 5) (6, 5) (8, 3)}and {(2, 1) (4, -1) (5, -1) (6, -1)} .

for each x-coordinate, plug it into the equation y = 3x + 11/3 and see which one gives out the matching y-value

for example, to test (4,5) let x = 4 and calculate y = 3x + 11/3 to see if you get 5

Answer 36

k