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3 years ago

PRE CALCULUS

Mathematics

1 answer:

Mumz [18]3 years ago

3 0

Start with the parent function f(x) = x³

Notice the function f(x) = (x - 4)³ that a value '4' is subtracted from 'x' ⇒ This means the function f(x) is translated four units to the right.

Then the function f(x) = ¹/₂ (x - 4)³, the function (x - 4)³ is halved vertically ⇒ Half the y-coordinate

Then the function f(x) = ¹/₂ (x - 4)³ + 5 that a value '5' is added to ¹/₂ (x - 4)³ ⇒ This means the function f(x) is translated five units up

So the order of transformation that is happening to f(x) = x³ is translation four units to the right, half the y-coordinate, then translate 5 units up.

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Answer:

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Step-by-step explanation:

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Answer this volume based Question. I will make uh brainliest + 50 points

Harlamova29_29 [7]

Answer:

$\huge{\purple {r= 2\times\sqrt[3]3}}$

$\huge 2\times \sqrt [3]3 = 2.88$

Step-by-step explanation:

For solid iron sphere:
radius (r) = 2 cm (Given)

Formula for $V_{sphere}$ is given as:

$V_{sphere} =\frac{4}{3}\pi r^3$

$\implies V_{sphere} =\frac{4}{3}\pi (2)^3$

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Formula for $V_{cone}$ is given as:

$V_{cone} =\frac{1}{3}\pi r^2h$

$\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)$

$\implies V_{cone} =\frac{1}{3}\pi (36x^3)$

$\implies V_{cone} =12\pi x^3\: cm^3$

It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume
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$\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}$

$\implies 12x^3= \frac{32}{3}$

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$\implies x={\frac{2}{ \sqrt[3]{3^2}}}$

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$\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}$

$\implies r=3\times 2(3)^{-\frac{2}{3}}$

$\implies r= 2\times (3)^{1-\frac{2}{3}}$

$\implies r= 2\times (3)^{\frac{1}{3}}$

$\implies \huge{\purple {r= 2\times\sqrt[3]3}}$
Assuming log on both sides, we find:

$log r = log (2\times \sqrt [3]3)$

$log r = log (2\times 3^{\frac{1}{3}})$

$log r = log 2+ log 3^{\frac{1}{3}}$

$log r = log 2+ \frac{1}{3}log 3$

$log r = 0.4600704139$

Taking antilog on both sides, we find:

$antilog(log r )= antilog(0.4600704139)$

$\implies r = 2.8844991406$

$\implies \huge \red{r = 2.88\: cm}$

$\implies 2\times \sqrt [3]3 = 2.88$

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Answer:

Step-by-step explanation:

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