Flight Characteristics "

$$\begin{matrix} \text{Type of Insect} & \text{Wing Beats (per second)} & \text{Flight Speed (kilometers per hour)}\\ \text{Hummingbird moth} & \text{85} & \text{17.8}\\ \text{Bumblebee} & \text{250} & \text{10.3}\\ \text{Housefly} & \text{190} & \text{7.1}\\ \end{matrix}$$

" -Based on the data, is there a relationship between the rate at which an insect beats its wings and the speed at which it flies? Explain. What factors besides wing-beat rate might affect flight speed?

Identify the letter of the word whose meaning is closest to that of the first word. effigies: (a) speeches, (b) insults, (c) dummies

Complete each statement. ? m = 3.01 km

"Rocket man" has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and is propelled straight upward. At a height of 16 m, his speed is 5.0 m/s. His mass, including the propulsion unit, has the approximately constant value of 136 kg. Find the work done by the force generated by the propulsion unit.

Solve each equation below. $\frac{5 x+4}{3}=\frac{2 x+1}{5}$

Determine whether the given value is a solution of the equation.

$$\frac{36}{x}=9 ; x=4$$

A local appliance store has decided on an advertising campaign utilizing newspaper and radio. Each dollar spent on newspaper advertising is expected to reach 50 people in the “Under $25,000” and 40 in the “Over$25,000” bracket. Each dollar spent on radio advertising is expected to reach 70 people in the “Under $25,000” and 20 people in the “Over$25,000” bracket. If the store wants to reach at least 100,000 people in the “Under $25,000” and at least 120,000 in the “Over$25,000” bracket, how should it proceed so that the cost of advertising is minimized? (a) Formulate a linear programming problem that models the problem. Be sure to identify all variables used. (b) Solve the linear programming problem. (c) Analyze the solution

Find the volume of the solid E whose boundaries are given in rectangular coordinates. E is bounded by the circular cone $z=\sqrt{x^{2}+y^{2}}$ and z=1.

The line y = 7 is the perpendicular bisector of the segment with endpoints A(2,10) and B(2,k). What is the value of k? Explain your reasoning.

Simplify each expression. $\left(\dfrac{3t^2}{5}\right)^2$

Estimate the value of each expression. $5\dfrac{1}{12}-2\dfrac{7}{9}$

use the quotient rule to derive $\frac{d}{d x}(\sec x)=\sec x \tan x$

What statement do you have to have in a value-returning function?

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve

$$y = e ^ { x }$$

, and the line x = ln 2 about the line x = ln 2.