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LenaWriter [7]
2 years ago
7

SUPER URGENT: Complete the general form of the equation of a sinusoidal function having an amplitude of 6, a period of 2pi/3, an

d a phase shift to the left 1 unit.
y =

Mathematics
1 answer:
mel-nik [20]2 years ago
4 0

Answer:

y = 6·sin(3·(x - 1)) + c

Step-by-step explanation:

The general form of an equation for a sinusoidal function is presented ad follows;

y = a·sin(b·(x - h) + c

Where;

a = The amplitude of the equation

T = The period = 2·π/b

h = The phase shift

c = The vertical shift

From the question, we have;

a = 6,

2·π/3 = 2·π/b

∴ b = 3

h = 1

We get;

y = 6·sin(3·(x - 1)) + c.

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The correct answer to your question is -2
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85 * 0.20 = 17
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Math question need help with substation please?
Juliette [100K]

<em>2 solutions</em>

<em>X= 16</em>

<em>X=49</em>

Step-by-step explanation:

<em>original equation</em>

<em>x-11√x+28 = 0</em>

<em>   Isolate</em>

<em>     -11√x = -x-28+0</em>

<em>  Tidy up</em>

<em>     11√x = x+28</em>

<em>  Raise both sides to the second power</em>

<em>     (11√x)2 = (x+28)2</em>

<em>After squaring</em>

<em>     121x = x2+56x+784</em>

<em> Plug in 49 for  x </em>

<em>      11√(49) = (49)+28</em>

<em>Simplify</em>

<em>      11√49 = 77</em>

<em>      Solution checks !!</em>

<em>     Solution is:</em>

     x = 49

<em>Plug in 16 for  x </em>

<em>      11√(16) = (16)+28</em>

<em>Simplify</em>

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3 0
3 years ago
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

V_{flask}=V_{sphere}+V_{cylinder}.

Use following formulas to determine volumes of sphere and cylinder:

V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

  • V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;
  • V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;
  • V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.

Then

\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.

Answer 2: correct choice is D.


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