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Maurinko [17]
2 years ago
4

( Melanie has 230 coins in her collection- Number of European and non-European coins)And now has 180 European coins. Write an eq

uation To determine the number of non-European coins, E, If Melanie has t total coins figure/find the Non-European coins and Identify the constant of proportionality. Pls show work thank you:/
Mathematics
2 answers:
katovenus [111]2 years ago
8 0

Total number of coins(including European and non European coins) =230

Number of European coins = 180

Let the number of non European coins be = E

T is the total coins or T =230

The equation to determine non European coins is

E=T-180

Solving this we get E=230-180=50

hence, E = 50


Leokris [45]2 years ago
4 0

Answer:

The amount of Non-Europeans coins is 50, and the constant of proportionality is approximately 0.217

Step-by-step explanation:

Let <u>T be the total of coins, E be the number of European coins, and nE be the number of non-European coins</u>, then

T=E+nE

so, <em>in order to know the amount of non-European coins</em> (nE), we clear nE from the equation

nE=T-E=230 coins-180coins=50coins

Finally, <em>the constant C of proportionality</em> is given by the following ratio

C=\frac{non-European}{Total}=\frac{nE}{T}=\frac{50}{230}\approx0.217

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=R\left(\frac {4x_1+3x_2}{7} , \frac {4y_1+3y_2}{7}\right).

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Answer:

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The boundary of integration is shown in the attachment.

Our first line integral is

L_1 = \int_ {(0,0)}^{(1,0)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

\therefore \: L_1 =0

Our second line integral is

L_2 = \int_ {(1,0)}^{(1,2)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is:

x = 0 \implies \: dx = 0

y varies from 1 to 2.

We substitute the boundary and the values to get:

L_2 = \int_ {1}^{2}1 \cdot y(0) +  {1}^{2}   \cdot \: {y}^{3} dy

L_2 = \int_ {1}^2 {y}^{3} dy =  \frac{8}{3}

The 3rd line integral is:

L_3 = \int_ {(1,2)}^{(0,0)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is

y = 2x \implies \: dy = 2dx

x varies from 0 to 1.

We substitute to get:

L_3 = \int_ {1}^{0} x \cdot \: 2xdx +  {x}^{2}  {(2x)}^{3}(2 dx)

L_3 = \int_ {1}^{0} 8 {x}^{5}  + 2 {x}^{2} dx  =  - 2

The value of the line integral is

L = L_1 + L_2 + L_3

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b) The second part requires the use of Green's Theorem to evaluate:

\int_C xydx +  {x}^{2}  {y}^{3} dy

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\int_C \: xydx + {x}^{2} {y}^{3}   \: dy =  \int_ 0^{1} \:  8{x}^{5} -  2 {x}^{2}   dx =  \frac{2}{3}

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