(d) Your next task is to find a curve which passes through (3, 5) in such a way that the gradient Vf(x, y) is tangent to the curve at every point on the curve, not just at (3, 5). Notice that your vector in part (b) NOT part (c) - has a vertical component, let's call that the "rise", and a horizontal component, which may as well be the "run". Now you know the slope of the tangent line to your dy curve at the point (3,5). From Calc 1, you know the slope is the derivative You now have da a (first-order) differential equation in x and y. Can you solve this equation? If not, that's okay. WolframAlpha will do that for you. What is the solution to this differential equation? (e) Your solution should have an arbitrary constant, C. Now, here's where the point (x, y) = (3,5) comes in. Use that (as your initial condition) to find your value of C.

Q: Sum-product pattern: (x + a)(x + b) = x² + (a + b)x + (a*b) x²+4x-12 (x+6)(x-2) a+b=4 a-b=-12…

A: The polynomial given isTo find:The factor of the given polynomial.Formula used:

Q: 4x²-16x + 16

A: Given that the expression we have to find the difference of square formula

Q: What is the domain of a polynomial?

A: We have to find the domain of polynomial function. We know that polynomial is defined as set of real…

Q: complete the squre -8x2-24x+16

A: Given,

Q: Write an equation for the polynomial graphed below 5 4 1+ -4 3 -2 -1 1 Y 3 4\5 -1 -3 -4 -5+ y = 3.…

A:

Q: Write an equation for the polynomial graphed below is t 13 -2 -1 AM 2 7 123456 -1 -2+ -3 -4 7 2 3 4…

A:

Q: Write in factored form. Determine the x-intercepts. y = x ^ 2 - 4x - 12

A: y= x2-4x-12We have to write y in factored formalso find x intercepts

Q: See attached image.

A: Vertex Form: a(x - h)2 + k = 0 we can use the formulas h=2a−b​ and  k=4a4ac−b2​  to convert the…