91Ó°ÊÓ

Sketch the graph of the equation in an \(x y z-\) coordinate system, and identify the surface. $$36 x=9 y^{2}+z^{2}$$

Approximate the horizontal and vertical components of the vector that is described. A child pulls a sled through the snow by exerting a force of 20 pounds at an angle of 40 with the horizontal.

Describe the region \(R\) in a three-dimensional coordinate system. $$ R=\left\\{(x, y, z): x^{2}+y^{2}+z^{2}>1\right\\} $$

Sketch the graph of the equation in an xyz-coordinate system. $$ x+y+z=0 $$

Sketch the graph of the equation in an \(x y z-\) coordinate system, and identify the surface. $$16 x^{2}+100 y^{2}-25 z^{2}=400$$

Verify without using components for the vectors. \((\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})=(\mathbf{a} \times \mathbf{b} \cdot \mathbf{d}) \mathbf{c}-(\mathbf{a} \times \mathbf{b} \cdot \mathbf{c}) \mathbf{d}\)

Describe the region \(R\) in a three-dimensional coordinate system. $$ R=\\{(x, y, z):|x| \leq 1,|y| \leq 2,|z| \leq 3\\} $$

Sketch the graph of the equation in an \(x y z-\) coordinate system, and identify the surface. $$x^{2}-16 y^{2}=4 z^{2}$$

Approximate the horizontal and vertical components of the vector that is described. A jet airplane approaches a runway at an angle of 7.5 with the horizontal, traveling at a velocity of \(160 \mathrm{mi} / \mathrm{hr}\)

Sketch the graph of the equation in an \(x y z-\) coordinate system, and identify the surface. $$3 x^{2}-4 y^{2}-z^{2}=12$$