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Vaselesa [24]
3 years ago
12

Write the first 4 terms of the sequence defined by the given rule f(n)=n2 -1

Mathematics
1 answer:
Softa [21]3 years ago
5 0

Answer:

<h2>0, 3, 8, 15</h2>

Step-by-step explanation:

Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:

f(1) = 1² - 1 = 1 - 1 = 0

f(2) = 2² - 1 = 4 - 1 = 3

f(3) = 3² - 1 = 9 - 1 = 8

f(4) = 4² - 1 = 16 - 1 = 15

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What are four key terms that can be used to describe Islam
horrorfan [7]

Answer:

Each of the four principles (beneficence, nonmaleficence,justice and autonomy) is investigated in turn.

Step-by-step explanation:

5 0
3 years ago
School A has 480 students and 16 classrooms. School B has 192 students and 12 classrooms.
boyakko [2]

Answer:96

Step-by-step explanation:

A; 480/16 = 30 students per classroom

B: 192/12 =16 students per classroom

we need x such that \frac{480-x}{16} = \frac{192+x}{12}

which means

(480-x )* 12 should be equal to (192+x) * 16

5,760 - 12x = 3,072+16x

5,760 - 3,072 = 12x + 16x

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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.


8 0
3 years ago
Read 2 more answers
Show all steps necessary to verify the trigonometric identity:
vekshin1

Answer:

1+tan2x

Tan2x

=      <u> sec²x  </u>        = <u>Sec²x  </u>       = cosec²x

    Tan²x            ( Sec²x/cosec²x)

Step-by-step explanation:

4 0
3 years ago
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