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1 year ago

Tom sells baseball cards at 10 for 35 cents. Is that better deal than 12 for 40 cents? Prove your thinking

Mathematics

1 answer:

Aleks [24]1 year ago

7 0

Answer:

12 for 40 cents is a better deal.

Step-by-step explanation: 35divided by 10 is 3.5 and 12 divided by 40 is 3.333... therefore for just one card it is cheaper but you are getting more cards anyways.

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A simple model for the shape of a tsunami is given by dW/dx = W √(4 − 2W), where W(x) > 0 is the height of the wave expressed

NeX [460]

Answer:

a) $W=0,2$

b) $W = 2 [1- tanh^2 (x+c)] = 2 sech^2 (x+c)$

Step-by-step explanation:

Part a

For this case we have the following differential equation:

$W \sqrt{4-2W}=0$

If we square both sides we got:

$W^2 (4-2W) =0$

And we have two possible solutions for this system $W=0, W=2$

So then that represent the constant solutions for the differential equation.

So then the solution for this case is :

$W=0,2$

Part b: Solve the differential equation in part (a)

For this case we can rewrite the differential equation like this:

$\frac{dW}{dx} =W \sqrt{4-2W}$

And reordering we have this:

$\frac{dW}{W \sqrt{4-2W}} = dx$

Integrating both sides we got:

$\int \frac{dW}{W \sqrt{4-2W}} = \int dx$

Using CAS for the left part we got:

$-tanh^{-1} (\frac{1}{2} \sqrt{4-2W})= x+c$

We can multiply both sides by -1 we got:

$tanh^{-1} (\frac{1}{2} \sqrt{4-2W})=-x-c$

And we can apply tanh in both sides and we got:

$\frac{1}{2} \sqrt{4-2W} = tanh(-x-c)$

By properties of tanh we can rewrite the last expression like this:

$\frac{1}{2} \sqrt{4-2W} = -tanh(x+c)$

We can square both sides and we got:

$\frac{1}{4} (4-2W) = tanh^2 (x+c)$

$1-\frac{1}{2}W = tanh^2 (x+c)$

And solving for W we got:

$W = 2 [1- tanh^2 (x+c)] = 2 sech^2 (x+c)$

And that would be our solution for the differential equation

3 0

2 years ago

There are 2000 pounds in a ton how can you write 2000 with and exponent

Makovka662 [10]

In scientific notation, it would be 2x10^3.
An easy trick to help remember when it is a multiple of 10 is that you do the numbers that aren't zero (2) times 10 and the exponent is how ever many zeros there are after the other numbers (3).

3 0

2 years ago

Read 2 more answers

Which decimal is equivalent to \dfrac{4}{3} 3 4 start fraction, 4, divided by, 3, end fraction? Choose 1 answer: Choose 1 answ

Otrada [13]

Answer:

The correct option is option D.

Step-by-step explanation:

Any fraction number $\frac mn$ (m>n ) can be written as $a\frac bn$

where a = quotient

b= reminder.

Given number is $\frac{4}{3}$ .

3)4( 1 ← quotient

- 3

____

1 ← reminder

Here quotient= 1, reminder=1 and n=3

$\therefore \frac43=1\frac13$ .

7 0

2 years ago

Jorge solves the equation 4x-(x+2)+6

Burka [1]

Answer:

Step-by-step explanation:

2x+6

Callie

4 0

2 years ago

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Melissa and Jane are planting trees. Melissa plants 10 trees in 1 hour. Jane plants 17 tree in 2 hours.

nadezda [96]

Answer:

6 hours

Step-by-step explanation:

Let both of them plan for t hours to plant 111 trees n t hours

Melissa can plants 10 trees in 1 hour

in t hours she can plant 10 t trees

Jane plants 17 tree in 2 hours

in one hour Jane can plant 17/2 trees

in t hours she can plant (17/2)t trees.

Total trees planted by both of them in t hours in terms of t will be

10t + (17/2)t

= (10t*2 + 17t)/2

= (20t + 17t)/2

= 37t/2

but it is given that they planted 111 trees together

so 37t/2 should be equal to 111

37t/2 = 111

=> 37t = 111*2 = 222

=> t = 222/37 = 6.

Thus, it takes 6 hours for both of them to plant 111 trees together.

4 0

2 years ago