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Basic Calculus

Multiplying Brackets, Simplifying & Model Rocket Height

1. (a) Perform the indicated operation and express the result in the form a + bi. (1 - i) (3 + i). (b) Simplify. i15 (c) x - 2y - 7 = 3x i + 5yi - 10 i 2. A model rocket is launched with an initial velocity of 100 feet per second from the top of a hill which is 20 feet high. Determine the time, t , that the rocke

Finding volume bounded by given curves

18. Compute the volume of the solid formed by revolving the region bounded by about (a) the x-axis; (b) y = 4. 20. Compute the volume of the solid formed by revolving the region bounded by and about (a) the y-axis; (b) x = 1. 4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, an

Solving a Set of Basic Mathematical Questions

See the attached file. 1. Write in radical notation and simplify if possible. 253/2 2. Assume all variables are positive real numbers. Write the following radicands with rational exponents and simplify if possible. 3. Solve for x (x + 2)(x - 2) = 15 + (x +1)(x - 7) Check your solution by substituting your solution

Integral Calculus Volume Problems

I need help with these two problems. If you could please explain the solution, I would appreciate it. 1.Use cylindrical shells to compute the volume. The region bounded by y = x and y = x2 - 2, revolved about x = 3 2. A solid is formed by revolving the given region about the given line. Compute the volume exactly if possi

Using Reimann Sums

Use the 'midpoint' rule for calculating the integral of x^3 on the domain [6,7] using n=2,5, and 10 equally wide rectangles. Then calculate the integral on the domain [2,4].

Calculus

Let f(x) = x^3, and compute the Riemann sum of f over the interval [6, 7], choosing the representative points to be the midpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) Two subintervals of equal length (n = 2) (b) Five subintervals of equal le

Spherical Trigonometry Proof

For a rectangular sperical triangle, where C = 90 degrees, show that: tan a = sin b tan A and, tan b = sin a tan B This is how far I have a gotten: sin C = 1 cos C = 0 I am also aware that I should be using both the Law of Cosines and the Law of Sines. Using these, I was able to prove several other identities. I am co

Solving Exact Differential Equations

(b) Find a suitable integrating factor R for the differential equation and verify whether the equation becomes exact after multiplying it by R. (c) Hence find the general solution of the differential equation. (See attached file for equations).

Stiff Spring Motion

Question: The displacement s cm of the end of a stiff spring at time t seconds is given by: s = a (e^−kt) sin 2πft. Determine the velocity and acceleration of the end of the spring after 2 seconds if a = 3, k = 0.75 and f = 20.

Minimize function

Suppose total transportation cost for a product can be approximated by the function: T(f) = 2.1f^2 - 25.9f +121.1 Where f is the number of facilities. Ignoring any other costs, find the optimal number of facilities with the minimum total transportation cost.

LPP - determinin objective function and inequalities

Formulate but do not solve the following linear programming problem. A travel company decides to advertise in the Saturday travel sections of two major newspapers in town. The advertisements are directed at three groups of potential customers. Each advertisement in newspaper A is seen by 60,000 group I customers, 35,000 group

Fourier series expansion - calculus

A function is defined as followed: see attachment Where f(t+2)=f(t) that is, f(t) has period 2. i) Draw a plot of the function f(t). Comment fully on whether the function is even or odd or none of these. ii) Find the first four non-zero coefficients for the Fourier series expansion of the function f(t) iii) Using eg. e

Characteristics of increasing graph

Describe the following characteristics of the graph shown in Graph3.pdf: 1. Where is the function increasing, decreasing, or constant? 2. Are there any relative/absolute extrema? If so, where? 3. Is the graph smooth or choppy (piecewise)? 4. Are there any restrictions on the domain? 5. Are there any horizontal or

Sketching the graph of a given function

Based on the information, create a sketch of the function on the axes provided. Please provide detailed explanation. ** Please see the attached file for the complete problem description ** -Increasing and constant: none -Decreasing: (-infinity, 2)... (please see the attached file) Thanks!

Quarterly compounding of interest

Kurt Daniels wants to buy a $30,000 car. He has saved $27,000. Find the number of years it will take for his $27,000 to grow to $30,000 at 4% interest compound quarterly. Please provide a detailed explanation.

Finding equations that represent exponential functions

Write an equation using the following information: Each represents an exponential function with base 2 or 3 translated and/or reflected 1) (-3,0), (-2,1), (0,7) Equation of horizontal asymptote: y=-1 2) (-1,3), (0,4), (-3,-3) Equation of horizontal asymptote: y=5

Derivatives and continuity of functions

1. Find the derivative of the function. h(t) = t2(3t + 9)3 2. Find the derivative of the function. 3. Find the derivative of the function. Find the derivative of the function. 4. f(x) = ex + e−x ------------ 2 Find the derivative of

Related Rates and calculus problems for real life situations

SEE ATTACHMENT FOR ALL PROBLEM QUESTIONS Related Rates Problems 1. A tiger escapes from a truck, right in front of the Empire State Building. I start running west along 34th Street at 2.5 m/s, while my friend takes off north on Fifth Avenue at 3 m/s. Draw a diagram of this situation. How fast is the distance between my

Cooling of soup

A bowl of soup at 185 degree F is left in a room with a temperature of 75 degree F to cool. - 0.075^t : After t minutes, the temperature, T, of the soup is given T(t)= 75 + 110e Find the temperature of the soup 24 minutes after it is left in the room (round to the nearest degree).

Pointwise limits f

Let fk (x) = sin (kx)/k k = 1, 2, 3, . . . . a) Determine the pointwise limit f of the sequence {fk} infinity k=1 on R. b) Show that the sequence {fk} infinity k=1 converges to f uniformly to f on R.

Calculating Probability of Selection

Please help with the following probability of selection problems. Provide step by step calculations. There are 1000 students in the senior class at a certain high school. The high school offers two advanced placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95

Bearing of a plane

A plane is heading due south with an airspeed of 231 mph. A wind from a direction of 53.0° is blowing at 12.0 mph. Find the bearing of the plane. (Note that bearings are measured from north, clockwise.) Round results to an appropriate number of significant digits.

Calculus: Related rates problem using a shoebox-shaped hall.

A multipurpose shoebox-shaped hall is planned. Its length is supposed to be x = 50 meters, the width is supposed to be y = 30 meters, and the height is 10 meters. Furthermore, an expensive diagonal beam is planned, hosting a movable camera car, starting in one (left, back, down) corner and going through the whole hall until

Calculating a vehicle's velocity and acceleration

Find the vehicle's velocity and acceleration at each of the following times. a) 1 second b) 10 seconds Please refer to the attachment to view the full question, including the velocity calculation to be used for this question.

Frequency Tables: Relative vs. Cumulative Frequencies

A website showing the reviews of different movies lists the films as follows, 5 five star films, 10 four star films 20 three star films 15 two star films and 5 one star films . Make a frequency table for the data set include columns for relative frequency and cummulative frequency.

PreCalculus: Average Rate of Change.

Please show work/explain answer. Not sure how to approach this question. Help please. 12) Find the average rate of change of the function: f(x) = (x + 1)2 between x = a and x = a + h Cannot figure out how to factor this equation to find zeros. Please help. 23) Show that x = 3 is a zero for x3 ? x2 ? 11x + 15,

Radius of Balloon Calculus Equations

1. A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters? 12. An air traffic controller spots two planes at the same altitude converging on a point as they fly at right a