1

dw dw For the functions w= - 7x + 7y", x= cost, and y= sint, express - as a function of t, both by using the chain rule and by expressing w in terms of t and differentiating directly with respect to t. Then evaluate att= - dw Express dt as a function of t. dw dtIf the equation F(x,y,z) =0 determines z as a differentiable function of x and y, then, at the points where F #0, the following equations are true. az and Use these equations to find the values of dz / dx and oz / dy at the given point. z" - xy + 2yz + 3y"-204 =0, (3,4,2) dz = (Type an integer or a simplified fraction.) dx (3,4,2)Among all the points on the graph of z = 8 - x- - y that lie above the plane x + 2y + 7z =0, find the point farthest from the plane. What are the values of x, y, and z for the point? X = by = 1, z= (Type integers or simplified fractions.)In constructing an open rectangular box from 867 fto of material, what dimensions will result in a box of maximum volume? Let x be the length of the box, let y be the width of the box, and let z be the height of the box. What is the equation that represents the total surface area of the box? Assume that the box is open on top.[23%) [23%) _ \"Sixth; (Ext)? nzxi it = n, where n is the number ofdata points: to nd the least squares line 1r = mx + h for the set of data points. Then use the linear equation to predict the value ofyr that would correspond to x: E. 1 Use the equations m = and lo: H (Eyk mzxk) with all sums running from k: 1 to [9.3] [1.2] [54) The least squares line is E. [Type an equation. Use integers or fractions for any numbers in the equation.)