What value is a discontinuity of $x$ squared plus $5 x$ plus $2$, all over $x$ squared plus $2 x$ minus $35$?

List the four characteristics that define an index fossil.

how do u solve y= negative x squared -14x-47? how do u solve y= negative 2x squared -2x-7? how do u solve y= 2/3x squared -4/5x?

Size the bevel gears in a $90^{\circ}$ straight bevel gearset is needed to give a $6:1$ reduction. Determine the pitch cone angles, pitch diameters, and gear forces if the $20^{\circ}$ pressure angle pinion has $20$ teeth of $p_{d}=8$, and the transmitted power is $3 \mathrm{~kW}$ at $900$ pinion $\mathrm{rpm}$. for a minimum safety factor of $1.8$ for any mode of failure of pinion or gear assuming a $5$-year, $2$-shift life, steady torque, quality index of $8$ , and an $\mathrm{AISI} ~4140$ steel pinion and gear.

A thin wire has the shape of a semicircle x squared + y squared =a squared, y greater than or equal to 0. Find the center of mass of the wire if the linear mass density of the wire at any point is proportional to its distance from the line y=a.

The index of refraction has the same units as velocity.

On a typical day, a city consumes water at the rate of

$$r(t) = 100 + 72 t - 3 t ^ { 2 }$$

(in thousands of gallons per hour), where t is the number of hours past midnight. What is the daily water consumption? How much water is consumed between 6 PM and midnight?

In an $RLC$ circuit a second capacitor is added in series to the capacitor already present. Does the resonance frequency increase, decrease, or stay the same? Choose the best explanation from among the following: I. The resonance frequency stays the same because it depends only on the resistance in the circuit. II. Adding a capacitor in series increases the equivalent capacitance, and this decreases the resonance frequency. III. Adding a capacitor in series decreases the equivalent capacitance, and this increases the resonance frequency.

How is the coefficient of performance of an absorption refrigeration system defined?

A torque of $40\ \mathrm{lb} \cdot \mathrm{ft}$ is applied through gear $A$ to the left end of the gear train shown in given figure. The diameters of gears $B$ and $C$ are 5 in. and 2 in., respectively. If the maximum shearing stresses in the aluminum alloy ( $G=3800\ \mathrm{ksi}$ ) shafts $A B$ and $C D$ are limited to $15\ \mathrm{ksi}$, find (a) The minimum permissible diameter for shaft $A B$. (b) The minimum permissible diameter for shaft $C D$. (c) The maximum length for shaft $C D$ if the rotation of a section at $D$ with respect to a section at $C$ must not exceed $0.5\ \mathrm{rad}$.

Find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points.

$$f (x, y) = (x − y)(xy − 1)$$

Explain what is wrong with the statement. If f has exactly two critical points, then one is a local maximum and the other is a local minimum.

Why do players take performance-enhancing drugs?

A large bowl contains 1 million marbles. Half of the marbles have a plus (+) painted on them and the other half have a minus (–). a. If you randomly sample 10 marbles, one at a time with replacement from the bowl, what is the probability you will select 9 marbles with pluses and 1 with a minus? b. If you take 1000 random samples of 10 marbles, one at a time with replacement, how many of the samples would you expect to be all pluses?