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calculate the flux of the
~F = (e−x2−y2)~k through the disk of radius 2 in the xy-plane, oriented upward.
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- Find the vector equation that represents the curve of intersection of the paraboloid z=3x^2+y^2 and the surface y=x^3. Write the equation so that one of the functions is simply t.Find the flux of the constant vector field i = - 4i - 5j-2k through a square plate of area 16 in the zy-plane oriented in the positive r-direction. flux =Find a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and the cylinder y=5x^2. Use the variable t for the parameter.r(t)=⟨t, , ⟩
- Find the flux of the constant vector field =-i-j+ k through a square plate of area 25 in the xy-plane oriented in the positive z- direction. flux =How do I find the flux of this vector field in the image attached?The position of a particle is determined by the vector-valued function r(t)=<1-t^2, 3t, t^3>. Find the decomposition of the acceleration vector in terms of its tangential and normal components when the particle is at the point (0,3, 1).
- Let the velocity vector be v(t)=⟨5t^4,−3sin(t),4exp(2t)⟩ and the initial position vector be r(0)=⟨−1,6,−1⟩. Compute the position vector r(t).A ball is thrown eastward into the air from the origin (in thedirection of the positive x-axis). The initial velocity is 50i+ 80k, with speedmeasured in feet per second. The spin of the ball results in a sounthwardacceleration of 4f t/s^2 , so the accelearation vector is a = −4j − 32k. Where does the ball land and with what speed?A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
- Sketch the vector field represented by F (x, y) = (-x,y)Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 3x2 + y2 and the parabolic cylinder y = 2x2 r(t) = (1,322 + 9^) * Need Help? Read ItCalculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect