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Anton [14]
4 years ago
14

Toby's piggy bank contains only 5c and 10c coins. If it contains 65 coins with a total value of 3.80, find the number of each ty

pe of coin.
Let x and y be the number of 5c and 10c coins respectively.
1a
Use the fact that the total number of coins is 65 to set up Equation 1.
Write the equation in the form ax+by=c, where a is positive.
Mathematics
1 answer:
mr_godi [17]4 years ago
5 0
The positive is 2 hknshue dska
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Solve the Differential equation 2(y-4x^2) dx + x dy = 0
padilas [110]

Assume a solution of the form \Psi(x,y)=C. Taking the differential of both sides would give the ODE

\Psi_x\,\mathrm dx+\Psi_y\,\mathrm dy=0

where \Psi_x=2y-8x^2 and \Psi_y=x. The ODE is exact if \Psi_{xy}=\Psi_{yx}. We have

\Psi_{xy}=(2y-8x^2)_y=2

\Psi_{yx}=(x)_x=1

so the ODE is not exact. However, multiplying both sides by x gives

(2xy-8x^3)\,\mathrm dx+x^2\,\mathrm dy=0

and now

(x\Psi_x)_y=(2xy-8x^3)_y=2x

(x\Psi_y)_x=(x^2)_x=2x

so the ODE is now exact.

Now,

\Psi_x=2xy-8x^3\implies \Psi(x,y)=x^2y-2x^4+f(y)

\Psi_y=x^2=x^2+f_y\implies f_y=0\implies f(y)=C

So the ODE has solution

\Psi(x,y)=x^2y-2x^4+C=C

or simply

\boxed{x^2y-2x^4=C}

3 0
4 years ago
In a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)?
Vesna [10]

Answer:

25 units

Step-by-step explanation:

Distance Formula: d = \sqrt{(x2-x1)^2+(y2-y1)^2}

Our points: (0, 0) and (7, -24)

d = \sqrt{7^2+(-24)^2}

d = √(49+576)

d = √625

d = 25

4 0
4 years ago
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What is the mixed number for 88/25?
marysya [2.9K]
SO, first you divide the numerator by the denominator. 

Then write it like this: \frac{88}{12}=  \frac{13 +3.25}{25} = 3 \frac{13}{25}.
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3 years ago
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ziro4ka [17]
From the first inequality x > 2 - 3  so x> -1
and from the second:-  x <= 4
so the graph will be a number line  with an open circle at x = -1 and a closed circle at x = 4  and  the line is shaded in between.
7 0
3 years ago
The components of vector a⃗ are ax = + 3.90 and ay = -4.00. What is the angle measured counterclockwise from the +x-axis to vect
Genrish500 [490]

The angle is the arctangent of the ratio of ay to ax. Since ay is negative and ax is positive, it is a 4th-quadrant angle.

... arctan(ay/ax) = arctan(-4.00/3.90) ≈ 314.27°

... about 5.48513 radians

3 0
4 years ago
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