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3 years ago

Help pls and thanks :)

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

4 0

Answer:

The two triangles can be considered similar as Angle A is 70 degrees and Angle B is a congruent angle to Angle A, which can be proven by adding 70 to 110 which shows a 180 degree angle (flat angle). Therefore we know that this triangle is similar

Step-by-step explanation:

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eimsori [14]

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Step-by-step explanation:

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3 years ago

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3 years ago

50 people sponsor Paula and she raises a total of $180.65 for charity. 28 people sponsor Kate and she raises a total of $135.60

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2 years ago

Determine if the field Bold Upper F equals 10 yz Bold i plus 10 xz Bold j plus 10 xy Bold k is conservative or not conservative.

Black_prince [1.1K]

F is conservative if we can find a scalar funciton f such that grad(f) = F.

This would entail

$\dfrac{\partial f}{\partial x}=10yz$

$\dfrac{\partial f}{\partial y}=10xz$

$\dfrac{\partial f}{\partial z}=10xy$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=10xyz+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=10xz=10xz+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiate both sides with respect to z :

$\dfrac{\partial f}{\partial z}=10xy=10xy+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C$

So we have

$f(x,y,z)=10xyz+C$

that satisfies

$\nabla f(x,y,z)=\mathbf F(x,y,z)$

and so F is indeed conservative.

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3 years ago