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Basic Calculus

Precalculus for technology is depicted.

7.4 #20 use an identity to write each expression as a single trigonometric function value or as a single number. 1-2sin^2(22)(1/2degree) #30 express each function as a trigonometric function of x. cos 3x #56 write each expression as a sum or difference of trigonometric functions. 8 sin 7x sin 9x #58 write each expression

Precalculus for technology is reiterated.

7.1 #2. if cos (theta) = -.65, then cos(-theta) = _______ #8. find sin (theta), cot (theta) = -(1/3), (theta) in quadrant IV #26 find the remaining five trigonometric functions of (theta), cos (theta) = (1/5), (theta) in quadrant I #56 write each expression in terms of sine and cosine, and simplify so that no quotients appea

Angular velocity question

a) A body of mass m kg is attached to a point by string of length 1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the point of attachment, calculate its angular velocity. b) If the mass rotates on a table, calculate the force on the table when the speed of rotation is 25 rpm and the mass is 6 kg.

Calculating Time Needed to Empty Tank

Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?

Equivalent impedance in radians

The equivalent impedance Z of two impedances Z1 and Z2 in parallel is given by the formula 1/Z = 1/Z1 + 1/Z2 . If Z1 = 3 + j2 and Z2 = 1 - j3, calculate Z giving your answer in the following form: r(cos 0 + j sin 0) where 0 is in radians. Take 0 as theta.

Convergent or Divergent

Determine whether the series is convergent or divergent by expressing the partial sum as a telescoping sum. If it is convergent, find its sum. The sum from n = 1 to infinity of 2 / (n^2 +4n +3).

Calculate the marginal cost

The total cost (in dollars) of producing x food processors is C(x)= 2500+90x-0.2x^2 (x-squared) (A) Find the exact cost of producing the 61st food processor. (B) Use the marginal cost to approximate the cost of producing the 61st food processor.

Calculus Example Question

In a certain memory experiment, subject A is able to memorize words at a rate given by (first attachment) In the same memory experiment, subject B is able to memorize at the rate given by (second attachment) How many more words does subject B memorize from t = 0 to t = 15 (during the first 15 minutes)? a. 16

Estimate the value of the quantity.

Estimate the value of the quantity. A piece of tissue paper is picked up in gusty wind. The table shows the velocity of the paper at 2 second intervals. Estimate the distance the paper travelled using Right-Endpoints. *** Table Is Attached *** Answer Options: a) 116ft b) 212ft c) 28ft d) 232ft

Velocity help

Velocity ds/dt (in meters/second) of a projectile is given by ds/dt=-9.8t+16 Find the displacement s of the object after 4 seconds if the initial displacement is 48m. Please show work

Velocity of a Propelled Object

If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per sec, then its height after t seconds is given by the equation h=-16t2+80t+96 where h is in feet. After how many seconds will the object reach a height of 196 feet?

Sample size: Penny abolition

A researcher wishes to estimate, with 90% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 2% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 24% of the respondents said they support abolishing the penny. b) No preli

Series Convergence: Determining Alpha Values

Fix a positive number alpha and consider the series: sum_{from k=1 to infinity} 1/([k+1][ln(k+1)]^alpha) For what values of alpha does this series converge? Please explain how the values of alpha were obtained. Please see attached document for the problem in equation form.

Simplifying Limits and DNE's

1. Evaluate the following limits. a) lim 2x^2 + 0x - 18/x^3 - 27=______. x->3 b) lim (9x + 6)^-1 - 24^-1/x - 2=_______. x->2 2. Let f(x)= {x^2 + 1, x<-4 {-3x + 2, -4<x<5 { 2/x, 5<x a) lim f(x)=________. x->-4^- b) lim f(x)=________. x->-4^+ c) lim f(x)=

Marginal Cost of Food Processors

The total cost (in dollars) of producing 'x' food processors is C(x)=2400 + 60x - 0.7x^2 (a) Exact cost of producing the 41st processor = 3.3 The part that I do not understand how to do: (b) Use the marginal cost to approximate the cost of producing the 41st food processor. I know I start off with: C'(x)=(d/dx) (2400

Differentiability in R^n

Suppose that 0<r<1 and than f: B(0) --> R is continuously differentiable. If there is an alpha>0 such that |f(x)|<=||x||^alpha for all xeB_r(0). Prove that here is an M>0 such that |f(x)|<=M||x|| for xeB_r(0)

Summation Notation to Infinity

Calc Questions & Answers 1) Make a List of 10 Mathish words or terms that were covered in this Calculus class and provide a brief definition (more than 10 words) 2) If Zero * Infinity is considered Non-Sense, What is Zero divided by Infinity? Give a 25 word or so explanation. 3) Write the sum 2 + 4 + 6 + .....+ 98 + 1

Find the average value for intervals

Consider the function f(x)= 4-x^2 a) Find the average value of f on the interval (0,2) b)Determine the number c that satisfies the mean value theorem for integrals for f on the interval (0,2) c)sketch the graph of f

Find the distance traveled.

A particle moves along a line so that its velocity at time t is v(t)= t^2-t-6 m/s a) Find the displacement of the particle during the time period 2< or equal to t< or equal to 4 and interpret the result. b) Find the distance traveled during this time period.

Derivatives and Trigonometry Functions

I need the full calculations as well as the answers. If I can see how you got from A to B to C I can figure it out, just the answers wouldn't help.10 basic problems. Find the First Derivative K(x)= 1/ (x^4)-(x^2)+1 G(t)= square root of 6t+5 G(x)= 6/[(3x^2)-1]^4 F(r)=[(r^2)-(r^-2)]^-2 Find the Limit lim

Liouville's theorem

Suppose that f(z) = u(x , y) + i*v(x, y) (where z = x + i*y) is ENTIRE and not constant. Use Liouville's theorem to prove that v(x, y) is unbounded. Under what conditions can a function that is harmonic everywhere be bounded?

Calculus: uniform continuity

Please refer to the attached file for the proper formatting. Suppose I C R and J C R are intervals, f : I --> J is uniformly continuous, and g : J --> R is uniformly continuous. a) Give the definition of h=g dot f. What is its domain? b) Prove that h is uniformly continuous.

Moment of Force Exerted in Mechanics

I'm having some trouble understanding how to get to the answer. The answer is in the book. -( 25.4 lb x ft)i - ( 12.60 lb x ft) j - ( 12.60 lb x ft) k . A 6- ft- long fishing rod AB is securely anchored in the sand of a beach. After a fish takes the bait, the resulting force in the line is 6 lb. Determine the moment about A

Perpendicular Difference Between Cables

I have some of the answers in my textbook. But I need help understanding the steps to get the answer. 1. 30.4 in. 3. F= -( 1220 N)I ; M = ( 73.2 N x m) j -( 122.0 N x m) k . 1. determine the perpendicular distance between cable EF and the line joining points A and D. 2. A dirigible is tethered by a cable attached to it

Determine angles and force of volleyball net

1. 43.6°. 2. M x = -31.2N x m; My = 13.20 N x m; Mz = -2.42 N x 3. Ǿ = 24.6°; d = 34.6 in. I'm having some problems with my work and need some assistance on how to get the answer. IF possible, please try to add some sort of diagram. 1. Consider the volleyball net shown. Determine the angle formed by guy wir

Finding Work Required To Empty a Tank: Example Problem

A tank in the shape of an inverted right circular cone has height 6 meters and radius 4 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot chocolate is d = 1030 kg/m3.

Volume Flow Rate for Laminar Flow in Pipe

The volume flow rate q (L^3 T-^1) for laminar flow in a pipe depends on the radius r (L) , the viscosity µ (M L^-1 T-^1) of the fluid, and the pressure drop per unit length dp/dz (M L^-2 T^-2) . a) Develop a model for the flow rate q as a function of r , µ , and dp/dz. b) How does q change if the radius is increa

Polynomial -- ball is thrown upwards......

If a ball is thrown upwards at 40 feet per second from a rooftop 24 feet above the ground, then its height above the ground t seconds after it is thrown is given by h = - 16 t2 + 40 t + 24. a. Rewrite the above formula with the polynomial on the right hand side factored completely. b. Use the factored version of the fo

Mathematics - Solving Calculus Equations

I really need help on these 4 problems and if you could please post your steps on how to do them, I'd greatly appreciate it. #1 Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y/dx2 at this point x=6t, y = &#8730;t, t = 1/25 The equation for the