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3 years ago

What is (4,-7) reflected on the x-axis

Mathematics

1 answer:

Furkat [3]3 years ago

8 0

Answer:

( 4, 7)

Step-by-step explanation:

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

A square plastic tarp has a perimeter of 68 meters. How long is each side of the tarp?

alina1380 [7]

Answer:

17 meters

Step-by-step explanation:

The perimeter is the addition of all sides. Since the perimeter is 68 meters and a square has 4 sides, we can divide 68 by 4 and we get 17.

7 0

2 years ago

Read 2 more answers

Function 1: y = 4x + 5 Function 2: The line passing through the points (1, 6) and (3, 10). Which of these functions has the grea

Gwar [14]

Answer:

Step-by-step explanation:

function 1 : y = 4x + 5

In y = mx + b form, which is what ur equation is in, the slope can be found in the m position. So the slope of this function is 4.

function 2 : (1,6),(3,10)

slope = (y2 - y1) / (x2 - x1)

(1,6)...x1 = 1 and y1 = 6

(3,10)...x2 = 3 and y2 = 10

now we sub

slope = (10 - 6) / (3 - 1) = 4/2 = 2

B. Function 1, because the slope is 4 and the slope of function 2 is 2. <==

8 0

2 years ago

Read 2 more answers

2 6/8 in simplest form

Vesna [10]

Answer:

2 3/4

Step-by-step explanation:

8 0

3 years ago

James correctly answered 85% of the 60 problems on his math test. How many questions did James answer correctly❄️

harina [27]

Answer:

James answered 51 questions correctly.

Step-by-step explanation:

1) Slide the decimal 2 places to the left in the percentage (85% = .85)

2) Multiply total by new decimal (60 x .85)

3) All done! (51)

Keep in mind that 100% is just 1 whole. Therefor 85% of one whole is .85. In this problem, 60 represents our whole.

3 0

2 years ago