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
IrinaVladis [17]
3 years ago
6

An art collector buys a replica of a famous sculpture. The replica has exactly the same shape as the original but is smaller. Th

e replica is 18 cm tall, and the the
original sculpture is 30 cm tall. If 189 cm of bronze was needed to make the replica, how much bronze was needed to make the original sculpture?
​
Mathematics
2 answers:
Luba_88 [7]3 years ago
4 0

Answer:

The answer is 315 cm of bronze

Step-by-step explanation:

yKpoI14uk [10]3 years ago
3 0

Answer:

315cm

Step-by-step explanation:

For this, we need to set up a proportion.

18/189=30/x

Cross multiply.

18x=189*30

18x=5670

Divide both sides by 18.

x=315

You might be interested in
Can someone check whether its correct or no? this is supposed to be the steps in integration by parts​
Gwar [14]

Answer:

\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

Step-by-step explanation:

\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}

Given integral:

\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x

\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:

\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x

Using <u>integration by parts</u>:

\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

Therefore:

\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}

\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:

\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)

\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}

\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}

Therefore:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x

\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:

\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}

Divide both sides by 2:

\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}

Rewrite in the same format as the given integral:

\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}

5 0
2 years ago
arrange the expressions in the correct sequence to rationalize the denominator of the expression -(2)/(\sqrt(x+y-2)-\sqrt(x+y+2)
cupoosta [38]
We have to rationalize the denominator:
\frac{-2}{ \sqrt{x+y-2} - \sqrt{x+y+2} } = \\  \frac{-2}{ \sqrt{x+y-2} -  \sqrt{x+y+2} }* \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-(x+y+2)}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-x-y-2}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2}  }{-4}= \\  \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{2}
6 0
2 years ago
Read 2 more answers
A translation is a type of transformation in which a figure is .
Romashka [77]

Answer:  Rotation

Step-by-step explanation:  can't be translation its tilted cant be reflection because of the tilt also cant be dilation because its the same size {hope this help's :{

7 0
3 years ago
Read 2 more answers
Find the area of the circle. Round to the nearest tenth. Use 3.14 or 22/7 for pie.
maks197457 [2]

Answer:

98.5 cm2

Step-by-step explanation:

6 0
3 years ago
Plssss answer this imma faillll :(((((
Zepler [3.9K]
U is right u gunna fail LOL
3 0
3 years ago
Other questions:
  • Write to fractions between 8/10 and 5/4​
    5·1 answer
  • X plus 1/3 equals nine enter your answer in the box in simplest form
    13·1 answer
  • jillian calculates that see will take 95 minutes to run 7 miles. she runs the distance in 80 minutes. what is jillians percent e
    12·1 answer
  • What is 3456 divide by 5
    6·2 answers
  • How do I solve 1/8x=5
    6·2 answers
  • PLEASE HELPPPP!!!!! need help with this
    5·1 answer
  • Select the correct answer from each drop-down menu.
    11·1 answer
  • Calculator
    15·2 answers
  • Please help!
    8·2 answers
  • Choose the best graph for the equation y=3x+2
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!