Solve the differential equation: (1+t2)t+i-tan-1t=0

Given the quadratic function f(x)=3x^2-24x+49 a. use “completing the squares” to convert the quadratic function into vertex form b. state the vertex c. find the x and y intercepts d. graph the function

Find the volume of the solid bounded by the plane z=0 and the paraboloid z=1-x^2 –y^2

Aproportional relationship between the number of pounds of carrots (x) and the price in dollars (y) is graphed, and the ordered pair (8, 6) is on the graphed line. part a: what is the price of 1 pound of carrots? show your work. (8 points) part b: what will the ordered pair (16, 12) on the graph represent? explain in words.