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LiRa [457]
3 years ago
10

Water begins to slowly leak from David’s water bottle right after he fills it. After 5 minutes, he notices the bottle has 26 oun

ces of water remaining. After 30 minutes, he notices the bottle has 16 ounces of water remaining. Let x represent the number of minutes that have passed and let y represent the amount of water remaining in the bottle.
Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0

Answer:

35y+5x=30

Step-by-step explanation:

iM biggest brain

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Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
13. Danny is in science class and is given a square block of metal with
jenyasd209 [6]

Answer: 336g.

Step-by-step explanation:

the formula for density is mass divided by volume (m/v). In this problem, you mus first find the volume of the square block. The formula for volume is length multiplied by width multiplied by height (LxWxH). To solve for volume you plug in the values to the equation: 6x4x2 = 48.

Now, you have the volume, and you have the density. Now you need to solve for mass. Plug in the values you have into the density equation (d=m/v):

7=m/48

to isolate M, multiply each side by 48. this leaves you with 7x48 = m. now all thats left is to solve. 7x48 = 336g. You can double check by plugging the values back into the equation. 336/48 = 7.

5 0
3 years ago
There is a box of colored marbles on the countertop. There are 24 blue, 16 green, and 32 red. What is the ratio of blue to total
labwork [276]

Step-by-step explanation:

........understood..............

8 0
2 years ago
Determine the unknown side lengths
Tems11 [23]

Answer:

Where is the shape?

Step-by-step explanation:

3 0
3 years ago
What is -2 square root of 20 negative square root of 125 in its simplest radical form
Ivenika [448]

Answer:

-7√5

Step-by-step explanation:

I'll transcribe your verbal question into a symbolic one as best I can:

-2√20 - √125

Note how √20 = √4*√5 and √125 = √25 *√5.  Thus,

your -2√20 - √125, after we've factored √5 out of both terms, becomes

-2(2)√5 - 5√5, or -2√5 - 5√5, which combines to form

-7√5 (answer)


7 0
3 years ago
Read 2 more answers
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