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2 years ago

Hi, help will be appreciated

Mathematics

1 answer:

aalyn [17]2 years ago

4 0

Answer:

KM=9

JK= 12.69

Angle JKM=45 degrees

ML=18.97

MKL=60 degrees

Angle L=30 degrees

Step-by-step explanation:

Triangle JKM is a 45, 45, 90 degree triangle so that means both side lengths are equal and the hypotenuse is square root of 2 times a side length. This means, KM will be equal to 9 and JK will be equal to 9 times square root of 2. For triangle KML, you know that the triangle is a 30,60,90 degree triangle. This means the hypotenuse is a^2+b^2=c^2 where c is the hypotenuse. Since you know that a is 9 and c is 21, plug them into the equation to get 81+b^2=441. Subtract 81 from both sides to isolate b^2 to get 360. b^2 = 360. Then find the square root of 360 which is about 18.97. Therefore, b or ML is equal to 18.97. Also, because we know that MKL is a 30, 60, 90 triangle, we know that angle MKL is equal to 60 degrees. Because we know the angles of MKL(60) and KML (90), we do 180-90-60 to find angle L. Simplify 180-90-60 to 30 and that means that angle L is equal to 30 degrees. Since we know that JKM is a 45, 45, 90 degree triangle, we know that JKM is equal to 45 degrees. Therefore, KM is equal to 9, JK is equal to 9 times square root of 2 or 9 times 1.41 which is 12.69. Angle JKM is 45 degrees, ML is 18.97, angle MKL is 60 degrees, and angle L is 30 degrees.

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

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