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3 years ago

8

owen has a collection of nickels and quarters worth $8.10. If the nickels were quarters and the quarters were nickels, the value

would be $17.70. Find the number of each coin.

1 answer:

prisoha [69]3 years ago

4 0

There are 67 nickels and 19 quarters.Im pretty sure

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The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli i

harina [27]

Answer:

a

$y(t) = y_o e^{\beta t}$

b

$x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

c

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

Step-by-step explanation:

From the question we are told that

$\frac{dy}{y} = -\beta dt$

Now integrating both sides

$ln y = \beta t + c$

Now taking the exponent of both sides

$y(t) = e^{\beta t + c}$

=> $y(t) = e^{\beta t} e^c$

Let $e^c = C$

So

$y(t) = C e^{\beta t}$

Now from the question we are told that

$y(0) = y_o$

Hence

$y(0) = y_o = Ce^{\beta * 0}$

=> $y_o = C$

So

$y(t) = y_o e^{\beta t}$

From the question we are told that

$\frac{dx}{dt} = -\alpha xy$

substituting for y

$\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })$

=> $\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt$

Now integrating both sides

$lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c$

Now taking the exponent of both sides

$x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}$

=> $x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c$

Let $e^c = A$

=> $x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

Now from the question we are told that

$x(0) = x_o$

So

$x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }$

=> $x_o = K e^{\frac {\alpha y_o }{\beta } }$

divide both side by $(K * x_o)$

=> $K = x_o e^{\frac {\alpha y_o }{\beta } }$

So

$x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

=> $x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }$

=> $x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

Generally as t tends to infinity , $e^{- \beta t}$ tends to zero

so

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

5 0

3 years ago

7x – 8y = 112 in slope intercept form

Digiron [165]

Answer:

y = 7/8x-14

Step-by-step explanation:

I found the answer to this on a website.

7 0

3 years ago

Read 2 more answers

.....................

Allisa [31]

Answer:

30

Step-by-step explanation:

We require to calculate the volume of 1 brick

V = lbh ( l is length, b is breadth and h is height ), that is

V = 14 × 8 × 5 = 560 cm³

Now divide the volume of concrete available by the volume of 1 brick.

number of bricks made = $\frac{16800}{560}$ = 30

5 0

3 years ago

Which Function rule describes the pattern in the table? x:-2,-1,0,1,2 / y:14,11,8,5,2 A) y=3x+8 B) y= -3x-8 C) y=3x-8 D) y=-3x+8

Leona [35]

For every value tht x increases, y decreases by 3

-3x

Then to find the y intercept, look at 0's corresponding value (8)

-3x+8

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3 years ago

|6t−7|−8 ≥ 3 Please help me quick

Phantasy [73]

Hope the answer helps you!!!
:)

5 0

3 years ago