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4 years ago

How do we do this? Please help....

Mathematics

1 answer:

polet [3.4K]4 years ago

7 0

Since s gets multiplied by 0.03, the rate of change is 0.03

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A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago

A number next to a variable always showd

Juliette [100K]

The number next to a variable, for example: 5x, is called a coefficient. And all you do is multiply the number with the variable

8 0

3 years ago

The subject of the formula below is y.<br>a=4x/t - p<br>Rearrange the f make x the subject.

Crazy boy [7]

Answer:

x = t(a+p)/4

Step-by-step explanation

Given the expression

a=4x/t - p

We are to make x the subject of the formula

a=4x/t - p

Add p to both sides

a+p = 4x/t - p+p

a+p = 4x/t

Cross multiply

t(a+p) = 4x

Rearrange

4x = t(a+p)

Divide both sides by 4

4x/4 = t(a+p)/4

x = t(a+p)/4

4 0

3 years ago

Find the slope of the line through each pair

Alekssandra [29.7K]

Answer:A) -4/3 B) 1/2 C) -5/4

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

For A) let (x1, y1) = (8, -7), (x2, y2) = (5, -3)

Slope = (-3 -(-7)) / (5 - 8) = 4/-3

For B) let (x1, y1) = (-5, 9), (x2, y2) = (5, 11)

Slope = (11 - 9) / (5 - (-5)) = 2/10 = 1/2

For C) let (x1, y1) = (-8, -4), (x2, y2) = (-4, -9)

Slope = (-9 -(-4)) / (-4 - (-8)) = -5/4

6 0

4 years ago

What is m∠2?<br> What is m∠1?

Greeley [361]

Answer:

<2 = 75

<1 = 105

Step-by-step explanation:

<2 and 75 are alternate interior angles and since the lines are parallel, they are equal

<2 = 75

<2 + <1 = 180 since the angles form a line

75+ <1 = 180

Subtract 75 from each side

<1 = 180-75

<1 = 105

6 0

3 years ago

Read 2 more answers