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Pepsi [2]
3 years ago
6

Ann has an empty cup and add 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how m

any seconds will they have the same amount of water
Mathematics
1 answer:
Lyrx [107]3 years ago
4 0

Answer:

4 seconds

Step-by-step explanation:

Given

Ann has an empty cup and add 1 ounce of water per second

let the number of seconds required to fill the cup be x

let the total be y

in x seconds Ann will have x ounces of water in the cup.

so the total amount of water in Ann's cup will be

y=x-----------1

Bob has 12 ounces of water and drinks 2 ounces per second

also, let the number of seconds required to empty the cup be x

let the total be y

y= 12-2x--------------2

Step two:

equate the two equations above and solve for x

x=12-2x

collect like terms

x+2x=12\\\\3x=12

divide both sides by 3

x=12/3\\\\x= 4 seconds

Therefore, after about 4 seconds Ann and Bob's cup will have the same amount of water

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2 years ago
Read 2 more answers
* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.
Sholpan [36]

The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.

Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars c_1,c_2,c_3 (not all zero) such that

c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)

which leads to the system of linear equations,

\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}

From the third equation, we have c_1=-c_2, and substituting this into the second equation gives

-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3

and in turn, c_1=c_3. Substituting these into the first equation gives

2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0

which tells us that any value of c_3 will work. If c_3 = t, then c_1=t and c_2 = -t. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.

Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.

3 0
1 year ago
The amount of stretch in a short bungee cord stretches 6 inches when stretched by a 3pound weight. A slinky stretches 3 feet whe
aleksklad [387]

Answer:

The slinky situation

Step-by-step explanation:

To make a rate, divide one value by the other.

For the short bungee,

6 inches ÷ 3 pound = 2 inches per pound

While the slinky,

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As you can tell by the numbers, 36 inches per pound is way better than the 2 inches per pound.

6 0
3 years ago
Tristan is 22 years younger than Sydney. 8 years ago, Sydney's age was 2 times Tristan's age. How old is Tristan now?
Serjik [45]

Answer:

Sydney is 52 years old, and Tristan is 30.

Step-by-step explanation:

Represent Tristan's age by t and Sydney's by s.

Then s - 8 = 2(t - 8), and t = s - 22

Substituting s - 22 in the first equation, we get:

s - 8 = 2(s - 22 - 8), or

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Solving for s:  -2s + s = -60 + 8, or -s = -52.

Sydney is 52 years old, and Tristan is 30.

4 0
2 years ago
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