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3 years ago

11

sam needs 4/6 cup of laundry detergent for his laundry. The cap on top of the laundry detergent holds 1/3 cup. He has 1 capful o

f detergent. Does he have enough explain.

1 answer:

uranmaximum [27]3 years ago

3 0

Simply 4/6 to its equivalent fraction of 2/3
Is 1/3 of a cup enough for the 2/3 a cup needed? No. So he doesn't have enough

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-2 (-3x + 3) + 2x = 58

dusya [7]

Answer:

x = 8

Step-by-step explanation:

Given

- 2(- 3x + 3) + 2x = 58 ← distribute and simplify left side

6x - 6 + 2x = 58

8x - 6 = 58 ( add 6 to both sides )

8x = 64 ( divide both sides by 8 )

x = 8

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2 years ago

If Clive was charged $3.92 for a minute 38 call, what is Clive's per minute base rate?

Tanzania [10]

Pretty sure it’s $0.10

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2 years ago

Arah went to the grocery store and bought 4 loaves of bread and 1 gallon of milk for $12. The next week, Sarah bought 2 loaves o

sergejj [24]

Answer:

Here, b represents one loaf of bread and m represents the one gallon of milk.

As per the statement:

Arah went to the grocery store and bought 4 loaves of bread and 1 gallon of milk for $12.

⇒ $4b+m = 12$

It is also given that the next week, Sarah bought 2 loaves of bread and 3 gallons of milk for $13.50.

⇒ $2b+3m = 13.50$

Then; system of equation :

$4b+m = 12$ .....[1]

$2b+3m = 13.50$ .....[2]

Solve for b and m using above system of equations.

Multiply equation [2] by 2 we get;

$4b+6m = 27$ .....[3]

Subtract equation [1] from [3] we get;

$4b+6m - 4b -m= 27-12$

Combine like terms;

$5m= 15$

Divide both sides by 5 we get;

m = $3

Substitute the value of m in equation [1] we get;

$4b+3 = 12$

Subtract 3 from both sides we get;

$4b=9$

Divide both sides by 4 we get;

b = $2.25

Therefore, cost of one loaf of bread (b) and one gallon of milk (m) are:

$2.25 ad $3

3 0

3 years ago

Describe the process of writing the equation of a line

lara [203]

If you are writing in slope-intercept form:

You first find the slope.

Put the slope in the equation.

Substitute any point into the equation and find the y-intercept.

7 0

3 years ago

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