please sketch the integral curves 021 →→→444 -0.2 4444 0.5 15 5 A direction field for y'= -(2xy² + y³) 25 77

Q3\ Determine the z transforms to the following : Z{sinh ka} *

Find the family of curves orthoganol to yi = xk

Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to prove? AXYZ by the SAS Similarity

Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (_. A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).

The graph of g(x) is shown below. The image includes two straight lines and a semi-circle. Use this image and geometry to evaluate each integral requested below. y=g(x) 2 4 2 (a) » g(z)dz= (b) (c) g(x)dr= » / g(z)dz= (d) 01

Find y" * y" at (1,1) of x'y =1

prove the theorem

Can someone help me with this please?

Use the method of Characteristic to solve Ut + 4tux = xu, u(x,0) = ex. Also draw a few characteristic curves. (Put x as the horizontal axis, and t as the vertical axis)