What is the percent of change in the cost of a hot dog?

Help me please with #12

Helga [31]

Answer:

Am am not that big brain

Step-by-step explanation:

6 0

3 years ago

Hey ya define matter have a great day

shutvik [7]

Answer:

matter is any substance that has mass and takes up space by having volume

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Determine whether the sequences converge.

Alik [6]

$a_n=\sqrt{\dfrac{(2n-1)!}{(2n+1)!}}$

Notice that

$\dfrac{(2n-1)!}{(2n+1)!}=\dfrac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\dfrac1{2n(2n+1)}$

So as $n\to\infty$ you have $a_n\to0$ . Clearly $a_n$ must converge.

The second sequence requires a bit more work.

$\begin{cases}a_1=\sqrt2\\a_n=\sqrt{2a_{n-1}}&\text{for }n\ge2\end{cases}$

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then $a_n$ will converge.

Monotonicity is often easier to establish IMO. You can do so by induction. When $n=2$ , you have

$a_2=\sqrt{2a_1}=\sqrt{2\sqrt2}=2^{3/4}>2^{1/2}=a_1$

Assume $a_k\ge a_{k-1}$ , i.e. that $a_k=\sqrt{2a_{k-1}}\ge a_{k-1}$ . Then for $n=k+1$ , you have

$a_{k+1}=\sqrt{2a_k}=\sqrt{2\sqrt{2a_{k-1}}\ge\sqrt{2a_{k-1}}=a_k$

which suggests that for all $n$ , you have $a_n\ge a_{n-1}$ , so the sequence is increasing monotonically.

Next, based on the fact that both $a_1=\sqrt2=2^{1/2}$ and $a_2=2^{3/4}$ , a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.

We have

$a_3=\sqrt{2\times2^{3/4}}=\sqrt{2^{7/4}}=2^{7/8}$
$a_4=\sqrt{2\times2^{7/8}}=\sqrt{2^{15/8}}=2^{15/16}$

and so on. We're getting an inkling that the explicit closed form for the sequence may be $a_n=2^{(2^n-1)/2^n}$ , but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.

Clearly, $a_1=2^{1/2}$ . Let's assume this is the case for $n=k$ , i.e. that $a_k$ . Now for $n=k+1$ , we have

$a_{k+1}=\sqrt{2a_k}$

and so by induction, it follows that $a_n$ for all $n\ge1$ .

Therefore the second sequence must also converge (to 2).

4 0

3 years ago

9.

RoseWind [281]

Answer:

C. I & III

Step-by-step explanation:

I simplifies to ...

2(6x +15 -5x) +4 = 40

12x +30 -10x +4 = 40

2x +34 = 40

__

II simplifies to ...

40 = 2(15 -x) +4

40 = 30 -2x +4

40 = -2x +34 . . . . . . not equivalent to I (sign of x-term is different)

__

III simplifies to ...

12x +30 -10x +4 = 40

2x +34 = 40 . . . . . . equivalent to I

___

I & III are equivalent

5 0

3 years ago

PPLEASE help due to tommarow I will mark as brainliest

natka813 [3]

Answer: 30 feet

--------------------------------

Work Shown:

x = height of tree in feet

The larger triangle, and the smaller triangle that fits inside the larger, are similr triangles.

So we can form the proportion
x/5 = 48/8
Note how x/5 is the result of dividing the larger vertical side (x) over the smaller vertical side (5)
The same applies with 48/8. The larger triangle's horizontal side is 8+40 = 48. The corresponding horizontal side for the smaller triangle is 8

Cross multiply to solve for x
x/5 = 48/8
8*x = 5*48
8*x = 240
8*x/8 = 240/8
x = 30

The tree is 30 feet tall

6 0

3 years ago