# College Statistics: alternate coordinate systems solving Recent questions in Alternate coordinate systems
Alternate coordinate systems
ANSWERED ### Convert the point from spherical coordinates to rectangular coordinates. $$(9, \pi, \frac{\pi}{2})$$ $$(x, y, z) = ?$$

Alternate coordinate systems
ANSWERED ### Consider the solid that is bounded below by the cone $$z = \sqrt{3x^{2}+3y^{2}}$$ and above by the sphere $$x^{2} +y^{2} + z^{2} = 16.$$.Set up only the appropriate triple integrals in cylindrical and spherical coordinates needed to find the volume of the solid.

Alternate coordinate systems
ANSWERED ### Descibe in words the region of $$\mathbb{R^{3}}$$ represented by the equation or inequality. $$y = -2$$

Alternate coordinate systems
ANSWERED ### Give a full answer for the given question: The covalent backbone of DNA and RNA consists of: ?

Alternate coordinate systems
ANSWERED ### The change - of - coordinate matrix from $$\mathscr{B} = \left\{\begin{bmatrix}3\\-1\\4\\\end{bmatrix}\begin{bmatrix}2\\0\\ -5 \\\end{bmatrix}\begin{bmatrix}8\\-2\\7\\ \end{bmatrix}\right\}$$ to the standard basis in $$RR^{n}.$$

Alternate coordinate systems
ANSWERED ### Describe in words the region of $$R^{3}$$ represented by the equation(s) or inequality. $$x = 5$$

Alternate coordinate systems
ANSWERED ### To explain^ Why the beta-coordinate vectors of $$\beta = {b_{1}, ... , b_{n}}$$ are the columns $$e_{1}, ... , e_{n}$$ of the $$n \times n$$ identity matrix.

Alternate coordinate systems
ANSWERED ### A subset $${u_{1}, ..., u_{p}}$$ in V is linearly independent if and only if the set of coordinate vectors $${[u_{1}]_{\beta}, ..., [u_{p}]_{\beta}}$$ is linearly independent in $$R^{n}$$

Alternate coordinate systems
ANSWERED ### Which of the following coordinate systems is most common? a. rectangular b. polar c. cylindrical d. spherical

Alternate coordinate systems
ANSWERED ### Plot the given point $$(-4, 0)$$ in a rectangular coordinate system.

Alternate coordinate systems
ANSWERED ### Give a full answer to given question: Double-stranded DNA looks a little like a ladder that has been twisted into a helix, or spiral. The side supports (poles) of the ladder are ?

Alternate coordinate systems
ANSWERED ### The vector x is in $$H = Span \ {v_{1}, v_{2}}$$ and find the beta-coordinate vector $$[x]_{\beta}$$

Alternate coordinate systems
ANSWERED ### Solve the given Alternate Coordinate Systems and give a correct answer 10) Convert the equation from Cartesian to polar coordinates solving for $$r^2$$: $$\frac{x^2}{9} - \frac{y^2}{16} = 25$$

Alternate coordinate systems
ANSWERED ### Describe in words the region of $$R^{3}$$ represented by the equation(s) or inequality. $$x^{2} + y^{2} = 4$$

Alternate coordinate systems
ANSWERED ### Show that the equation represents a sphere, and find its center and radius. $$x^{2} + y^{2} + z^{2} + 8x - 6y + 2z + 17 =0$$

Alternate coordinate systems
ANSWERED ### What coordinate system is suggested if the integrand of a triple integral involves $$x^{2} + y^{2}?$$

Alternate coordinate systems
ANSWERED ### Let C be a circle, and let P be a point not on the circle. Prove that the maximum and minimum distances from P to a point X on C occur when the line X P goes through the center of C. [Hint: Choose coordinate systems so that C is defined by $$x2 + y2 = r2$$ and P is a point (a,0) on the x-axis with a $$\neq \pm r,$$ use calculus to find the maximum and minimum for the square of the distance. Don’t forget to pay attention to endpoints and places where a derivative might not exist.]

Alternate coordinate systems
ANSWERED ### Describe in words the region of $$RR^{3}$$ represented by the equation or inequality. $$z \geq -1$$

Alternate coordinate systems
ANSWERED ### Use a graphing calculator to graph the solution of the system of inequalities. Find the coordinates of all vertices, rounded to one decimal place. $$\begin{cases}y \geq x - 3\\y \geq -2x+6\\y \leq 8\end{cases}$$
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