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2 years ago

Select the correct answer.

Mathematics

1 answer:

crimeas [40]2 years ago

8 0

Answer:

Step-by-step explanation:

The absolute value function always returns a positive value, that is

| - a | = | a | = a

Given

8 - | 2g - 5 | ← substitute g = - 3.5 into the expression

= 8 - | - 7 - 5 |

= 8 - | - 12 |

= 8 - 12

= - 4 → D

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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

Please help 6th grade math i will give brainliest to answer with worked shown

Wewaii [24]

Answer:

Step-by-step explanation:

She drinks 4 ounces every 30 minutes.

4*2= 8 She drinks 8 ounces in an hour.

8*8=64 She drinks 64 ounces in 8 hours

8 0

2 years ago

Choose the inequality whose solution set is represented by this graph

alexgriva [62]

Answer:

LETTER A

Step-by-step explanation:

I think it's correct

6 0

2 years ago

What is the slope of the line that passes through the following points (7,10) and (10,9)

Svet_ta [14]

Answer:

-1/3

Step-by-step explanation:

To find the slope, we can use the slope formula

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

= ( 9-10)/(10-7)

= -1/3

8 0

3 years ago

Read 2 more answers

What is the equation of the midline for the function f (x)? f (t) = 3 cos (x) – 2.5

zaharov [31]

Answer:

y = -2.5

Step-by-step explanation:

For such a problem as this, you can replace all sine or cosine functions with their midline value of 0. Then you have ...

f(x) = 0 -2.5

which simplifies to ...

f(x) = -2.5

You can leave the equation like this, or write it as ...

y = -2.5

_____

Perhaps you can see that the midline is the value of any constant added to a sine or cosine function.

6 0

2 years ago