1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ira [324]
3 years ago
15

The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Det

ermine each of the following, showing all your work and reasoning.
Scale factor of the smaller pyramid to the larger pyramid in simplest form

Ratio of the areas of the bases of the smaller pyramid to the larger pyramid

Ratio of the volume of the smaller pyramid to the larger

Volume of the smaller pyramid
Mathematics
1 answer:
tatiyna3 years ago
7 0
\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\


\bf \cfrac{smaller}{larger}\qquad \cfrac{\stackrel{height}{6}}{\stackrel{height}{12}}\implies \cfrac{1}{2}\impliedby \textit{scale factor of the pyramids}\\\\
-------------------------------\\\\
\cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt{base}}{\sqrt{base}}\implies \cfrac{1}{2}=\sqrt{\cfrac{base}{base}}\implies \left( \cfrac{1}{2} \right)^2=\cfrac{base}{base}
\\\\\\
\cfrac{1^2}{2^2}=\cfrac{base}{base}\implies \cfrac{1}{4}=\cfrac{base}{base}\\\\
-------------------------------\\\\

\bf \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt[3]{volume}}{\sqrt[3]{volume}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{volume}{volume}}
\\\\\\
\left( \cfrac{1}{2} \right)^3=\cfrac{volume}{volume}
\implies 
\cfrac{1^3}{2^3}=\cfrac{volume}{volume}\implies \cfrac{1}{8}=\cfrac{volume}{volume}\\\\
-------------------------------\\\\
\cfrac{smaller}{larger}\qquad \cfrac{1}{8}=\cfrac{\stackrel{volume}{v}}{\stackrel{volume}{400}}\implies \cfrac{1\cdot 400}{8}=v
You might be interested in
Select the correct answer.<br> Which of these graphs represents a function?
enyata [817]

Answer:

W.

Step-by-step explanation:

Because it's a cubic function which means it has to be a function because it literally has function in it.

7 0
2 years ago
write an equation of the line passing through point p that is perpendicular to the given line p(6,10),y=-3x+13
patriot [66]

Answer:

y = \frac{1}{3} x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 3x + 13 is in this form

with m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-3} = \frac{1}{3}

y = \frac{1}{3} x + c ← is the partial equation

To find c substitute (6, 10) into the partial equation

10 = 2 + c ⇒ c = 10 - 2 = 8

y = \frac{1}{3} x + 8 ← equation of line


6 0
3 years ago
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 9 k
nadya68 [22]

Answer:

6 kg

Step-by-step explanation:

Given is weight of an object directly varies with the mass of the object .

Let the constant of proportionality be k

So,

Weight = K×(mass of the object)

For an object , weight = 45 N

                        mass = 9 kg

So , 45 = K×9

      K = 5.

Now, for the other object ,

Weight = 30 N. K = 5 (as obtained above)

So, 30 = 5×(mass of the object)

mass of the object = 6 kg.

5 0
3 years ago
What is the common ratio in this geometric series?
Lerok [7]
For a geometric sequence or geometric series, the common ratio is the ratio of a term to the previous term. This ratio is usually indicated by the variable r. Example: The geometric series 3, 6, 12, 24, 48, . . . has common ratio r = 2.
4 0
3 years ago
Estimation is best defined as: a. both a process of inferring the values of unknown samples statistics from those of known popul
Ghella [55]

Answer:

Option D is the correct answer - Estimation is best defined as   a process of inferring the values of unknown samples statistics from those of known population parameters

Step-by-step explanation:

Estimation involves the usage of the value of a statistic derived from a sample to estimate the value of a corresponding population parameter.

The sample provides information that can be extended, through several formal or informal processes, to determine a range most suitable to describe the missing information.

An estimate that turns out to be incorrect would either be termed as over-estimation or under-estimation. If the estimate exceeds the actual result, it is termed as an over-estimation, and as an under-estimation, if the estimate came short of the actual result.

Thus, option D is correct.

8 0
3 years ago
Other questions:
  • With a real machine, why is W out always smaller than W in
    6·1 answer
  • Consider this topic for a survey: How far do students at Alpha Elementary jump? Which of the following would lead to a biased sa
    5·1 answer
  • If you walk 10 miles in 10 hours, how fast are you going?
    6·2 answers
  • Please be quick! I need this as soon as possible !
    13·1 answer
  • What is the interquartile range of the data? What is the range of the middle half of the data? What is the range of the data? Wh
    10·2 answers
  • The circle shown has a radius of 12 mm
    11·1 answer
  • 1⁄2 × 1⁄5 = ....whats this answer
    13·2 answers
  • I HIT 80 SUBS !!!!! if you want to help out my yt is 999 Trendy TYSMMMM ill give brainliest if u help. hope i get helpes :(
    9·1 answer
  • The difference of a number and 19 is 22.
    9·2 answers
  • In the month of May 2019, Norfolk International Airport
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!