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Ratling [72]
3 years ago
8

If lines p and q are reflected across the x-axis, then which of the pairs of lines shown would coincide with this transformation

?
A. lines a and b
B. lines c and d
C. lines f and e
D. lines g and h

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

the answer is C. ) lines f and e

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An oblique cylinder has a radius of 9 centimeters and a volume of 486 cubic centimeters. Use Cavalieri’s Principle to calculate
kotegsom [21]

Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

<h3>What is the height of the oblique cylinder?</h3>

From Cavalieri's principle, the volume of an oblique cylinder is expressed as;

V = base area × h

V = πr² × h

Given that;

  • Radius r = 9cm
  • Volume of the oblique cylinder V = 486πcm³
  • Height of the oblique cylinder h = ?

V = πr² × h

486πcm³ = π × ( 9cm )² × h

486πcm³ = π × 81cm² × h

486πcm³ = 81πcm² × h

h = 486πcm³ / 81πcm²

h = 6cm

Using Cavalieri’s Principle, the height of the oblique cylinder with the given volume and base radius is 6cm.

Option A) is the correct answer.

Learn more on volume of cylinder here: brainly.com/question/16788902

#SPJ1

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What are the period and phase shift for f(x) = −4 tan(x − π)?
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\bf ~~~~~~~~~~~~\textit{function transformations}&#10;\\\\\\&#10;% function transformations for trigonometric functions&#10;% templates&#10;f(x)=Asin(Bx+C)+D&#10;\\\\&#10;f(x)=Acos(Bx+C)+D\\\\&#10;f(x)=Atan(Bx+C)+D&#10;\\\\&#10;-------------------

\bf \bullet \textit{ stretches or shrinks}\\&#10;~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\&#10;\bullet \textit{ flips it upside-down if }A\textit{ is negative}\\&#10;~~~~~~\textit{reflection over the x-axis}&#10;\\\\&#10;\bullet \textit{ flips it sideways if }B\textit{ is negative}

\bf ~~~~~~\textit{reflection over the y-axis}&#10;\\\\&#10;\bullet \textit{ horizontal shift by }\frac{C}{B}\\&#10;~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\&#10;~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\&#10;\bullet \textit{vertical shift by }D\\&#10;~~~~~~if\ D\textit{ is negative, downwards}\\\\&#10;~~~~~~if\ D\textit{ is positive, upwards}

\bf \bullet \textit{function period or frequency}\\&#10;~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\&#10;~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)

with that template in mind, let's see this one.

\bf f(x)=\stackrel{A}{-4}tan(\stackrel{B}{1}x\stackrel{C}{-\pi })+\stackrel{D}{0}&#10;\\\\\\&#10;\stackrel{period}{\cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi }&#10;\\\\\\&#10;\stackrel{phase/horizontal~shift}{\cfrac{C}{B}\implies \cfrac{-\pi }{1}}\implies -\pi \qquad \textit{shifted to the right by }\pi \textit{ units}
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3 years ago
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