A metal sphere of radius 30 cm has a net charge of

$$3.0 \times 10 ^ { - 8 } C$$

. (a) What is the electric field at the sphere's surface? (b) If V = 0 at infinity, what is the electric potential at the sphere 's surface? (c) At what distance from the sphere's surface has the electric potential decreased by 500 V?

For the given functions f and g, (a) Graph f and g on the same Cartesian plane. (b) Solve f(x) = g(x). (c) Use the result of part (b) to label the points of intersection of the graphs of f and g. (d) Shade the region for which f(x) > g(x), that is, the region below f and above g. $f(x)=-x^{2}+4 ;\ g(x)=-2 x+1$

Find all irreducible polynomials of degrees $1,2,4$ over

$$\mathbb{F}_2$$

and prove that their product is $x^{16}-x$.

A neutral solid metal sphere of radius 0.1 m is at the origin, polarized by a point charge of $6 \times 10^{-8}\ \mathrm{C}$ at location $\langle- 0.3,0,0\rangle\ \mathrm{m} .$ At location $\langle 0,0.07,0\rangle\ \mathrm{m},$ what is the electric field contributed by the polarization charges on the surface of the metal sphere? How do you know?

Did any of the statements in “Of Marriage and single Life” surprise you? Explain why.

Women usually have higher resistance of their arms and legs than men. Why might you expect to see this variation in resistance?

Compare: (a) 0.31 ? 0.301 (b) 31% ? 30.1%

What voltage is involved in a 1.44-kW short circuit through a $0.100 - \Omega$ resistance?

Determine how parameter a affects the solution. Solve the generic equation y’ = ax + y. How does varying a change the behavior?

Several studies have shown that β-carotene, a precursor of vitamin A, may play a role in preventing cancer. β-Carotene has a molecular formula of

$$C_{40}H_{56}$$

, and it contains two rings and no triple bonds. How many double bonds does it have?

What do you make of lines 19-22? Are these two statements logical? Do they sound true to you?

Most centroid calculations for curves are done with a calculator or computer that has an integral evaluation program. As a case in point, find, to the nearest hundredth, the coordinates of the centroid of the curve

$$x = t ^ { 3 } , \quad y = 3 t ^ { 2 } / 2 , \quad 0 \leq t \leq \sqrt { 3 }.$$

The disk method can be used in any situation in which the washer method is successful at finding the volume of a solid of revolution.

Use a graphing utility to graph the curve $x^{2}+y^{2}=\sqrt{x^{2}+y^{2}}+x.$ Find the equation of each horizontal tangent to the curve. (The curve is called a cardioid.)