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2 years ago

At a yard sale, you buy a box, of 240 football and baseball cards.

Mathematics

1 answer:

Mekhanik [1.2K]2 years ago

3 0

Answer:

720 baseball cards⚾

Step-by-step explanation:

240 = football cards

240 times 3 = baseball cards⚾

240

x 3

______

720

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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

Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20 degrees and angel BCA measures 30 degree

alexdok [17]

The image of the question is attached below.

Given:

m∠DAC = 20° and m∠BCA = 30°

m∠ABC = 90° and m∠CDA = 90°

To find:

The value of x and y.

Solution:

In right triangle ABC,

m∠BAC = x° + 20°

Sum of the interior angles of a triangle = 180°

m∠BAC +m∠ABC + m∠BCA = 180°

x° + 20° + 90° + 30° = 180°

x° + 140° = 180°

Subtract 140° from both sides.

x° + 140° - 140° = 180° - 140°

x° = 40°

In right triangle ADC,

m∠ACD = y° + 30°

Sum of the interior angles of a triangle = 180°

m∠ACD +m∠CDA + m∠DAC = 180°

y° + 30° + 90° + 20° = 180°

y° + 140° = 180°

Subtract 140° from both sides.

y° + 140° - 140° = 180° - 140°

y° = 40°

The value of x is 40 and y is 40.

6 0

2 years ago

The Green Lawns Company uses the equation C=82.75a+56 to determine the amount to charge for mowing a city park, where a is the n

ratelena [41]

Answer: The significance of the number 82.75 in the equation = amount charged per acre in the park.

Step-by-step explanation:

Given: The Green Lawns Company uses the equation C=82.75a+56 to determine the amount to charge for mowing a city park, where a is the number of acres in the park and C is the cost in dollars.

In linear equation y=mx+c, = rate of change of y with respect to x.

Here Coefficient of a = rate of change of C with respect to a.

i.e. Coefficient of a =amount charged per acre in the park.

Hence, The significance of the number 82.75 in the equation = amount charged per acre in the park.

7 0

2 years ago

Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?

____ [38]

Answer:

A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.

Step-by-step explanation:

-4.4 ≥ 1.6 x - 3.6

Solving for the value of x,

1.6 x ≤ -4.4 + 3.6

1.6 x ≤ - 0.8

Dividing 1.6 from both sides to know value of x

x ≤ - 0.5

8 0

2 years ago

Read 2 more answers

Do the numbers show a pattern 11.23,10.75,10.3,9.82,9.37,8.89

sattari [20]

Answer:

is this a yes or no question

7 0

2 years ago