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3 years ago

Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X L с D A) 44 B) 34 C) 31 D) 29

Mathematics

1 answer:

adell [148]3 years ago

5 0

Step-by-step explanation:

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What is the slope of a line perpendicular to the line whose equation is 3x+y=-5

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Answer:

tdy

Step-by-step explanation:

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3 years ago

Please ONLY Answer #3

Fynjy0 [20]

Answer:

yes , keiko is correct.

sin^(-1)x = -sin^1

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2 years ago

Read 2 more answers

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eimsori [14]

Right triangles have 3 sides and can be named according to an angle other than the 90 degree one. They are named opposite, adajacent, and hypotenese.
Then use SOHCAHTOA.
SOH means sin equals opposite/hypotunse.
CAH means cosine equals adjacent/hypotnuse.
TOA means tagent equals opposite/adjacent.
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2 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.

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

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.

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

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.

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

so $\vec F$ is not conservative.

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

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

Bill hiked 4 miles than 3 times the amount hit friend hiked. Write an expression that represents the amount of miles bill has hi

Yuki888 [10]

Answer:

x3 + 4

Step-by-step explanation:

Scince Bill's friends amount of miles is unkown its x, and times it by three since it says times, and then add 4 since it says more than! Hope this helps! There is a really good website called Khan Academy and it explains everything! Just search in google your topic and say khan academy at the end and you will get practices and videos! Good luck!

5 0

3 years ago

Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X L с D A) 44 B) 34 C) 31 D) 29​

Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X L с D A) 44 B) 34 C) 31 D) 29