{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

moreF12practice

Iii if we project p to the yz plane we get a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: iii. If we project P to the yz plane, we get a parallelogram in the yz plane. What is the area of that parallelogram? 7. Suppose R is the parallelipiped spanned by u = h a; ; i ; v = h b 1 ; b 2 ; i ; w = h c 1 ; c 2 ; c 3 i . i. Give a formula for the surface area A in terms of a; b 1 ; b 2 ; c 1 ; c 2 ; c 3 . ii. Give a formula for the volume V in terms of a; b 1 ; b 2 ; c 1 ; c 2 ; c 3 . iii. If we wanted to nd the parallelipiped with maximal volume among all such parallelipipeds with the same surface area A , write (but don't solve) the Lagrange multipliers system in the variables a; b 1 ; b 2 ; c 1 ; c 2 ; c 3 that we'd need to solve. iv. By examining the equations in the Lagrange multipliers system, show that u ; v ; w must be mutu- ally orthogonal to maximise volume. ( Hint. Consider @ @b 1 V = @ @b 1 A .) 8. TRUE or FALSE. For each of the following statements, indicate whether it is true (T) or false (F). Support your answers. i. The graph of a solution of the di erential equation dy dt = cos y is a sinusoidal wave. ii. The graph of a solution of the di erential equation dy dt = sin t is a sinusoidal wave. iii. The curve r ( t ) = h 1 4 t 3 2 ; 4 t 3 ; cos( t 2) i is tangent to the surface x 3 + y 3 + z 3 xyz = 0 at the point (0 ; 1 ; 1)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online