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Vlad [161]
3 years ago
9

Prove that an = 4^n + 2(-1)^nis the solution to

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
4 0

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute a_n=4^n+2(-1)^n in the equation a_n=3a_{n-1}+4a_{n-2} the equality is true.

Let's substitute first in the right hand side:

3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})

Now we use the distributive laws. Also, note that (-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n} (this also works when the power is n-2).

=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}

=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}

=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n

then the sequence solves the recurrence relation.

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dimulka [17.4K]

Answer:

9 and 16

Step-by-step explanation:

let the two numbers are X and Y

X+Y=24

X^2-Y^2=144

solve simultaneously

4 0
3 years ago
How many centimeters (cm) are in 1 inch?
ivolga24 [154]
<h2><u>ANS</u></h2>

<h3>1 inch = 2.54 <u>cm</u> </h3>

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8 0
2 years ago
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Simplify 7(2x+y)+6(×+5y)
iris [78.8K]

Simplify, <em>7(2x+y)+6(x+5y).</em>

<em>a:</em> <em>20x+37y</em>

<em> (7 • (2x + y)) +  6 • (x + 5y) </em>

<em>Step  2  : </em>

<em>Equation at the end of step  2  : </em>

<em>  7 • (2x + y) +  6 • (x + 5y) </em>

<em>Step  3  : </em>

<em>Final result : </em>

<h3><em> </em><em> 20x + 37y</em></h3>

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Hi there!

\large\boxed{D. \text{ }y = -4x + 6}

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slope = \frac{y_{2}-y_{1}}{x_{2}-x{1}}

Plug in the corresponding coordinates:

slope = \frac{-6-2}{3-1}

Simplify:

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Therefore, we have:

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Plug in the x and y values for a coordinate to solve for b:

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The equation is:

y = -4x + 6. The correct answer is D.

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3 years ago
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