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Arisa [49]
3 years ago
9

Find the point slope equation for the line that passes through the points (2,1) and (-2,5). use the first point in your equation

.
y- [?]=[?](x-[?])
Mathematics
2 answers:
Delicious77 [7]3 years ago
4 0

Answer:

y - 1 = -(x - 2)

Step-by-step explanation:

y - y1 = m(x - x1)

m = (5-1)/(-2-2) = 4/-4 = -1

Using any one coordinate, construct

y - y1 = m(x - x1)

y - 1 = -1(x - 2)

stiks02 [169]3 years ago
3 0

Yo sup??

By applying slope point formula ie

y-y1=m(x-x1)

we get

m=y2-y1/x2-x1

=5-1/-2-2

=-1

y-1=-1(x-2)

y+x=3

Hope this helps

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2x(6x^2 + 3x - 1)<br><br> Simplify
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Answer: 12x^3+ 6x^2- -2x
6 0
3 years ago
55 mi / h = ____ ft / s <br> a. 8.7 <br> c. 80.7 <br> b. 26.9 <br> d. 806.7
Tcecarenko [31]
The answer is c. If the answer is wrong i am sorry
4 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
4 years ago
Please help me it needs to be correct
dimaraw [331]

Answer:

4(3m^3-2m^2+4m+2)

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Maya and Mabel are inspecting an 80:1 scale floor plan of their new house. The dimensions of the living room on the scaled floor
AveGali [126]

Answer:

208 ⅓ ft²

Step-by-step explanation:

1⅞ = 15/8 inches ÷ 12

= 5/32 feet on map

Actual = 5/32 × 80

= 25/2 feet

2½ = 5/2 inches ÷ 12

= 5/24 feet on map

Actual = 5/24 × 80 = 50/3

Actual area:

25/2 × 50/3

= 625/3 ft²

= 208 ⅓ ft²

4 0
3 years ago
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