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Brums [2.3K]
2 years ago
5

Mila and samuel had an equal amount of money for shopping. Mila spent $42 and Samuel spent $36. After that, Mila had 1/2 of what

Samuel has left. How much money Milla had initially?
Mathematics
1 answer:
koban [17]2 years ago
6 0

Answer:

Mila had $48 initially

Step-by-step explanation:

Let the amount of money they had be x

Mila spent $42; what is left would be x-42

Samuel spent $36: what is left would be x-36

So, what Mila had left is half of what Samuel has; that would be;

x-42 = 1/2(x-36)

2(x-42) = x -36

2x-84 = x -36

2x - x = 84 -36

x = $48

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Triangle ABC is an oblique triangle. If angle A equals 57°, angle B equals 73°, and AB equals 24 in, what is the length of AC?
natulia [17]

Step-by-step explanation:

\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}

Angle C must = [180 - 73 - 57 ] = [180 - 130] = 50°

And using rhw Law if Sines, we have.....

AB/sin C = AC/sin B → 24/sin(50) = AC/sin(73) → AC = 24*sin(73)/sin(50) = about 29.96 in

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3 years ago
I need help
agasfer [191]
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How many liters will a U.S. 6-quart container hold? Round your answer to the nearest hundredth
vovikov84 [41]
<span>You are given volume of 6 US quart. You are required to convert this into liters and be rounded off to the nearest hundredth.  Keep in mind that for volume, every one liter is equal to 1.05669 US quart. So you need to divide the 6 US quart. This is equal to 6.34014 liters. To round of the nearest hundredth, the ocation of the hundredth is the four in 6.3<u>4</u>014. since after four is zero, the round off rule states that from 0-4, the preceding number remains unchanged. So the final answer is 6.34 liters.</span>
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3 years ago
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For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
3 years ago
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Leto [7]
<h3>Answer:</h3>

y=kx

Step-by-step explanation:

That's the formula for direct variation relationships!

The other two answers are nonsense and don't mean anything.

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