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Analytic geometry

### Trace the curve $$\displaystyle{y}=\frac{{x}}{{{x}-{1}}}{\left({x}+{3}\right)}$$

Analytic geometry

### Trace the curve $$\displaystyle{r}^{{2}}={4}{{\cos}^{\theta}{{\tan}^{{2}}\theta}}$$

Analytic geometry

### Find an equation of the plane passing through the three points given. P = (2, 0, 0), Q = (0, 4, 0), R = (0, 0, 2)

Analytic geometry

### Given two rectangles: 15m by 7m and 27m by 3m. Find the combined area.

Analytic geometry

### The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of $$\displaystyle\pi$$ and then round to two decimal places.

Analytic geometry

### Let v = zk be the velocity field of a fluid in $$\displaystyle{R}^{{3}}$$. Calculate the flow rate through the upper hemisphere (z > 0) of the sphere $$\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}={1}.$$

Analytic geometry

### Express $$\displaystyle{\tan{\theta}}$$ in terms of $$\displaystyle{\sin{\theta}}$$.

Analytic geometry

### Consider the line represented by the equation 5x + 2y = 10. How is the slope of the line related to values of A, B, and C in standard form Ax + By = C?

Analytic geometry

### Given a right triangle. One of the angles is $$\displaystyle{20}^{\circ}$$. Find the other 2 angles.

Analytic geometry

### The vertices of a tetrahedron correspond to four alternating corners of a cube. By using analytical geometry, demonstrate that the angle made by connecting two of the vertices to a point at the center of the cube is $$\displaystyle{109.5}^{\circ}$$, the characteristic angle for tetrahedral molecules.

Analytic geometry

### You're riding a bicycle with 13-inch radius wheels. When the speed is 44ft/sec, how many revolutions are her wheels making per one minute?

Analytic geometry

### The measure of an angle is 6 less than 5 times its complement. What is the measure of the complement?

Analytic geometry

### Circulation of two-dimensional flows Let C be the unit circle with counterclockwise orientation. Find the circulation on C of the following vector fields. a. The radial vector field $$\displaystyle{F}={\left\langle{x},{y}\right\rangle}$$ b. The rotation vector field $$\displaystyle{F}={\left\langle-{y},{x}\right\rangle}$$

Analytic geometry

### A circle is inscribed in a right triangle. The length of the radius of the circle is 6 cm, and the length of the hypotenuse is 29 cm. Find the lengths of the two segments of the hypotenuse that are determined by the point of tangency.

Analytic geometry

### Point K is on line segment ‾JL. Given JK = 2x - 2, KL = x - 9, and JL = 2x + 8, determine the numerical length of ‾KL.

Analytic geometry

### Trace the curve of $$\displaystyle{x}^{{3}}-{6}{x}^{{2}}+{11}{x}-{y}={6}$$

Analytic geometry

### What id the circumference of the circle? use $$\displaystyle\frac{{22}}{{7}}$$ for $$\displaystyle\pi,{r}={21}$$ cm

Analytic geometry

### What are verticle angles?

Analytic geometry