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2 years ago

TJ is think of a number which he calls n he finds 1/3 of the number

Mathematics

2 answers:

Andrew [12]2 years ago

8 0

Answer:

Step-by-step explanation:

Let the number TJ thinks of be n.

If he finds 1/3 of the number, the expression that models this situation is expressed as:

1/3 of n

= 1/3 * n

= n/3

hence the expression that models the scenario is n/3

rosijanka [135]2 years ago

7 0

Answer:

1/3n-5

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

The volume V of a cone varies jointly as the area of the base B and the height

seraphim [82]

Answer:

h = 9 cm.

Step-by-step explanation:

V = kBh where k is the constant of variation.

From the given info:

32 = k*16*6 = 96k

So k = 32/96 = 1/3.

So we have the equation of variation:

V = 1/3Bh

When V = 60 B = 20, so:

60 = 1/3 20h

20h = 60 * 3 = 180

h = 180 /20 = 9.

3 0

2 years ago

8x = 96 How would I solve for x

Vaselesa [24]

How to solve your problem

6 0

2 years ago

Read 2 more answers

2. If AB = 4x + 9. BC = 5x + 2, and AC = 56, then find the value for . AB, BC. A B

inysia [295]

Answer:

AB=29; BC=27

Step-by-step explanation:

So they told us AB=4x+9 and that BC=5x+2, and AC=56 , now to help with the question you can draw this information on a number line. Now on a number you can see that basically AC=AB+BC.

So you would write it as such,,

4x+9+5x+2=56

Combine like terms

9x+11=56

Now you have to isolate the x by itself but first get rid of the 11.

9x+11-11=56-11

You would get

9x=45

Here you can divide 9 by both sides to isolate x.

9x/9=45/9

{x=5}

Now to find the value for both substitue x in the equations for both

1. AB=4x+9 where x is 5

4(5)+9 =AB

20+9 =AB

29=AB

You would do the same with BC

2. BC= 5x+2 where x is 5

5(5)+2= BC

25+2= BC

27=BC

If you want to check your answers you can just substitute x for 5 in the first equation we did where AC=AB+BC

6 0

3 years ago

What is the correct answer? Please provide an explanation.

ryzh [129]

Answer:

A 270° rotation about point B'

Step-by-step explanation:

Rotation is clockwise so you can see that the final transformation is a rotation 270° clockwise

4 0

3 years ago

Read 2 more answers