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n200080 [17]
3 years ago
7

Charlotte runs a farm stand that sells bananas and raspberries. Each pound of bananas sells for $3.25 and each pound of raspberr

ies sells for $1.75. Charlotte sold 13 more pounds of bananas than pounds of raspberries and made $227.25 altogether. Determine the number of pounds of bananas sold and the number of pounds of raspberries sold.
Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
4 0

Answer:

50 pounds of bananas

37 pounds of raspberries

Step-by-step explanation:

3.25(b) + 1.75(b - 13) = 227.25

5b - 22.75 = 227.25

5b = 250

b = 50

b - 13 = 37

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A ramp slopes from a warehouse door down to the street. The height of the ramp is 5 feet, and the ramp ends 10 feet from the bas
Tomtit [17]
If you graph this, your first point will be at (0,5), as the ramp is at the warehouse door but 5 feet up. The second point is (10,0) as it is touching the ground but it's 10 feet away from the warehouse.
To find slope, you do (y2-y1)/(x2-x1).
When substituting in the variables, you get (0-5)/(10-0), which is -5/10, which is simplified to -1/2. Of course, that is when the warehouse is Quadrant II. If you look at it from another point of view, the slope will be positive so your answer is A) 1/2.
If this was unclear feel free to comment :)
3 0
3 years ago
Read 2 more answers
Help me please i dont understand this question..
stich3 [128]
5x6 = 30 divided in half because its a triangle
=15

2x3 = 6

15-6 = 9
4 0
2 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
Im not sure if anyone knows how to do this but if u do could u pleaseee help me with this!!!
slavikrds [6]

Answer:

y = -2x - 5

Step-by-step explanation:

<u>1) Find the slope of the line.</u>

The slope of the original line is the same as the slope of the parallel line.

Slope formula:

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

In this case you can choose any 2 set of points on the table.

m = \frac{4 - 2}{-3 - (-2)} = \frac{4 - 2}{-3 + 2} = \frac{2}{-1} = -2

So the slope of the line is -2

<u>2) Use the point-slope formula to find the equation of the line.</u>

Point-slope formula:

y - y_{1}  = m(x - x_{1})

Now plug in the point (0, -5) and the slope -2 into the equation.

y - (-5) = -2(x - 0)

y + 5 = -2(x - 0)

To solve the equation first apply the distributive property.

y + 5 = -2x + 0

y + 5 = -2x

Next, subtract 5 from sides.

y = -2x - 5

You know have your equation in point-slope form!

6 0
3 years ago
What is 6/4 simplified
Rashid [163]
Since this is an improper fraction, you simplify it into a mixed number. 
4 goes into 6 1 time. 2 left left over, resulting in 1 2/4. Simplify that into 
1 1/2
6 0
3 years ago
Read 2 more answers
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