4

Mathematics

1 answer:

HACTEHA [7]1 year ago

7 0

Answer:

True

Step-by-step explanation:

x - 4y = 11 → (1)

- 3x + 5y = 25 → (2)

Multiply (1) by 5 and (2) by 4 to eliminate the y- term

5x - 20 y = 55 → (3)

- 12x + 20y = 100 → (4)

Add (3) and (4) term by term to eliminate y

- 7x + 0 = 155

- 7x = 155 ← y- term is eliminated

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3 0

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$\displaystyle\bf\\Explanations:\\\\The~similarity~ratio~of~two~similar~cones=k\\\\k=is~the~ratio~between~2~corresponding~lengths\\\\k=\frac{R_1}{R_2}=\frac{h_1}{h_2}\\\\The~ratio~between~2~corresponding~areas~of~similar~cones=k^2\\\\\frac{Area~1}{Area~2}=k^2\\\\The~ratio~between~the~volumes~of~the~2~similar~cones=k^3\\\\\frac{Volume~1}{Volume~2}=k^3$

$\displaystyle\bf\\Solving:\\\\Volume1=108~m^3\\\\Volume2=4m^3\\\\k^3=\frac{108}{4}\\\\k^3=27~~\Big|\sqrt{~}\\\\k=\sqrt[\b3]{27}\\\\k=3\\\\Area1=54~m^2\\\\\frac{Area~1}{Area~2}=k^2\\\\\frac{54}{Area~2}=3^2\\\\\frac{54}{Area~2}=9\\\\Area2=\frac{54}{9}\\\\\boxed{\bf Area2=6 m^2}$