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3 years ago

Subtract the second of the following expression from the first a-b+c-d, c-a+d-b

1 answer:

6 0

First: a-b+c-d
Second: c-a+d-b
First-Second
=a-b+c-d-(c-a+d-b)
=a-b+c-d-c+a-d+b after distributing the negative sign
=a+a-b+b+c-c-d-d collect similar terms
=2a-0+0-2d
=2a-2d

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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

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3 years ago

Cost of a pen o.95 mark up 60

Alika [10]

I think the answer is 5700

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4 years ago

Write sin 29 degrees 32 minutes in terms of it cofunction

12345 [234]

Answer:

Sin 29° 32' = Cos 60° 28'

Step-by-step explanation:

Here in this problem, we have to write Sin 29° 32' in terms of its co-function.

We know that co-function of Sin Ф = Cos ( 90° - Ф ).

Therefore, we have to find a complementary angle of 29° 32'.

So, ( 90° - 29° 32' ) = 60° 28'

Therefore, Sin 29° 32' = Cos 60° 28' ( Answer )

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3 years ago

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

LenKa [72]

Answer:

Step-by-step explanation:

120 is the starting value, aka the price of the painting in 2014 before it is increased.

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3 years ago

What is the value of x? 27(x+4)=−6

jonny [76]

First you need to use the distributive property: 27(x+4)=-6
27x+108=-6
then you need to subtract 108 from -6 to
get x alone. 27x= 102

Lastly divide 102 by 27 to finally get x alone: x=3.777

the answer would be: x= 3.77 or 3.8

5 0

4 years ago