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3 years ago

The object on the right is made from a square based pyramid...

Mathematics

1 answer:

natima [27]3 years ago

8 0

Answer:

$7.81\ g/cm^3$

Step-by-step explanation:

step 1

Find the volume of the cuboid

The volume is equal to

$V=(6^2)(9)=324\ cm^3$

step 2

Find the mass of the cuboid

Remember that

The density is equal to divide the mass by the volume

The mass is equal to multiply the volume by the density

$m=(324)(0.68)=220.32\ g$

step 3

Find the mass of the square base pyramid

subtract the mass of the cuboid from the total mass

$970-220.32=749.68\ g$

step 4

Find the volume of the pyramid

The volume is equal to

$V=\frac{1}{3}(6^2)(8)= 96\ cm^3$

step 5

Find the density of the steel (pyramid)

divide the mass of the pyramid by the volume of the pyramid

$749.68/96=7.81\ g/cm^3$

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Please check the attached graph.

From the graph, it is clear that option B is the correct option.

Step-by-step explanation:

Given the function

$g\left(x\right)=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x$

Determining the y-intercept

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

substituting x = 0 in the fuction

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^x$

$y=\:\frac{3}{2}\:\left(\frac{2}{3}\right)^0$

Apply rule: $a^0=1,\:a\ne \:0$

$y=1\cdot \frac{3}{2}$

$y=\frac{3}{2}$

$y = 1.5$

Therefore, the point representing the y-intercept is:

(0, 1.5)

Determining the x-intercept

We know that the value of the x-intercept can be determined by setting y = 0, and determining the corresponding value of x.

substituting y = 0 in the function

$0=\frac{3}{2}\left(\frac{2}{3}\right)^x$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$\left(\frac{2}{3}\right)^x=0$

We know that $a^{f\left(x\right)}$ can not be zero or negative for x ∈ R

Thus, NONE represents the x-intercept.

Please check the attached graph.

From the graph, it is clear that option B is the correct option.

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