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2 years ago

13

If a pattern starts with one and doubles each term(1,2,4,8,16...) what is the algebraic pattern rule from y(term value) to x(ter

m number)?

1 answer:

grin007 [14]2 years ago

7 0

Answer:

Step-by-step explanation:

y=a(r)^{n-1}

y=1(2)^{x-1}

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Answer:

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Step-by-step explanation:

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2 years ago

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fgiga [73]

Answer:

The answer to |4a|=20 is a=5 or a=-5.

Step-by-step explanation:

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2 years ago

Describe the set of points z in the complex plane that satisfy the given equation; |z-2|=Re(z).

OLEGan [10]

Answer:

Parabola with vertex at point (1,0) that goes to the right (see attached diagram).

Step-by-step explanation:

Let the complex number z be

$z=x+iy,$

then

$z-2=x+iy-2=(x-2)+iy\\ \\Re\ (z-2)=x-2\\ \\Im\ (z-2)=y\\ \\|z-2|=\sqrt{Re^2\ (z-2)+Im^2\ (z-2)}=\sqrt{(x-2)^2+y^2}$

and

$Re\ z=x$

Thus,

$\sqrt{(x-2)^2+y^2}=x$

Square it:

$(x-2)^2+y^2=x^2\\ \\x^2-4x+4+y^2=x^2\\ \\-4x+4+y^2=0\\ \\y^2=4x-4\\ \\y^2=4(x-1)$

This is the equation of parabola with vertex at point (1,0) that goes to the right.

3 0

2 years ago

Zigmanuir [339]

Answer:

Ai. Arithmetic sequence

Aii. Tn = 5 + 7n

Bi. Geometric

Bii. Tn = 8 × 2ⁿ¯¹

Step-by-step explanation:

To successfully answer the questions given above, note the following:

1. If the sequence is Arithmetic, then:

2nd – 1st = 3rd – 2nd = common difference (d)

2. If the sequence is geometric, then,

2nd / 1st = 3rd / 2nd = common ratio (r)

3. A sequence can not be arithmetic geometric at the same time.

4. The nth term of arithmetic sequence is:

Tn = a + (n – 1)d

5. The nth term of geometric sequence is:

Tn = arⁿ¯¹

A. Sequence => 12, 19, 26

i. Determination of the type of sequence.

We'll begin by calculating the common difference

1st term = 12

2nd term = 19

3rd term = 26

Common difference (d) = 2nd – 1st

d = 19 – 12 = 7

OR

d = 3rd – 2nd

d = 26 – 19 = 7

Since a common difference exist in the sequence, the sequence is arithmetic sequence.

ii. Determination of the nth term.

Common difference (d) = 7

1st term (a) = 12

nth term (Tn) =?

Tn = a + (n – 1)d

Tn = 12 + (n – 1)7

Tn = 12 + 7n – 7

Tn = 5 + 7n

B. Sequence => 8, 16, 32

Bi. Determination of the type of sequence.

Let us begin by calculating the common ratio.

1st term = 8

2nd term = 16

3rd term = 32

Common ratio (r) = 2nd / 1st

r = 16 / 8

r = 2

OR

r = 3rd / 2nd

r = 32 / 16

r = 2

Since a common ratio exist in the sequence, the sequence is geometric.

Bii. Determination of the nth term.

Common ratio(r) = 2

1st term (a) = 8

nth term =?

Tn = arⁿ¯¹

Tn = 8 × 2ⁿ¯¹

8 0

2 years ago