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Basic Calculus

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

Foot building a man observes a car moving toward him

From the top of a 200 foot building a man observes a car moving toward him. If the angle of the car changes from 35 degrees to 60 degrees during the period of observation, how far does the car travel? Round to the nearest tenth.

Differentiation and Graphing

Consider the curve xy^2 + y = 3 - x^2. Use implicit differentiation to find the derivative dy/dx Hence determine the tangent to the curve at the point (-2,1) A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 0.5ms-1. How rapidly is the area enclosed by the ripple inc

Rate of Change Problem

An airplane that is taking off due North is ascending at a rate of 75 feet per second with a land speed of 500 miles per hour. If this airplane is positioned 3 miles east of an observer on the ground when it takes off, how quickly is the angle of elevation from the observer changing after 3 minutes?

Calculus problems

Assignment Problem 1 Given f(x)=x^2+2x+3 Find the difference quotient (f(x+h)-f(x))/h Use the definitional formula given below to find the derivative of the function. f^' (x)=lim?(h?0)??(f(x+h)-f(x))/h? Find the value of the derivative at x = 3. Word-process your solution below. ? Assignment Problem 2 Given,

Internet Resources

The Internet offers many resources to support mathematics instruction. Conduct a search for websites that offer free mathematics resources (e.g., math activities, games, and/or lessons for students). Choose at least one site, provide a summary of its offerings, and evaluate the effectiveness of these offerings in reinforcing mat

Curvilinear motion

A ski jump is design to follow the path given by the equations: x=3.5t^2 and y=20.0+0.120t^4 - 3.00 sqrt(t^4+1) (0 less than or equal to (t) less than or equal to 4.00 s) ( x and y in m, t in s). Find the velocity and acceleration of a skier when t = 4.00 seconds.


A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water.) Part 2: A layer of water Δx m thick which lies x m above the bottom of the tank will be rectangular with length 8 m. Using similar triangles, what will the width be?

Calculus Growth: Ferret Population Example

A family of ferrets start with 10 individuals but grows at a rate of six percent per year compounded semi-annually. Develop a mathematical relationship showing the population of ferrets, y, in any year as a function of years, x. a. Construct the dataset and compute values of y for x=0, 1, 2, 3, 4, 5, 6. Graph the function o

Total Cost to Produce Products

Homework Set 17: Problem 2 Section 5.5, Problem 3 Section 5.5, Problem 12 Section 5.5 Section 5.5: Problem 3 pg. 262 3. The total cost in dollars to produce q units of a product is C(q). Fixed costs are $20,000. The marginal cost is C'(q)= 0.005q2 -q+56 A. On a graph of C'(q), illustrate graphically the total varia

Inflection Points/Algebra

Homework Set 8: Problem 10 Section 4.1, Problem 10 Section 4.2 Section 4.2: Problem 10 pg. 180 For f(x) = x3 -18x2 -10x +6, find the inflection point algebraically. Graph the function with a calculator or computer and confirm your answer. (For the exponents, it is x cubed and -18x squared).

Resideu theorem

Show that integral from 0 to infinity of 1/(x^3+1)dx=2pi(sqrt3)/9 by integrating 1/(z^3+1) around circular sector 0<thetha<2/3pi and 0<r<p and let p go to infinity

Solve the following systems of equations

Solve the following systems of equations <!--[if !supportLists]-->- <!--[endif]-->4x+7y=-6(y+5) and 6(x-6)=8x-y <!--[if !supportLists]-->- <!--[endif]-->4(b+2)=-6b-c and 8(b-7)=3-7c

calculus problems

Parabola in the figure is given by: f (x) 0.5x^2 - x + 1.5 Consider the straight lines given by: y = 0.5x + b The figure is plotted three straight lines with three different b-values, namely, 1.0, -1 ie. y = 0.5x +1 y = 0.5x y = 0.5x -1 a) Calculate for b = 1.5 coordinate the set for each of the intersections betw

Please help me with the calculus problems.

We have the function f(x,y) = e^(-x^2 + y^2) : a. To draw some level curves; b. Calculate the gradient and determine the stationary points; c. To write the equation of the tangent plane to z = f(x,y) in the point (0, 0, f(0, 0)), and in the point A (1,1,f(1,1)); d. To write the Taylor formula of f(x,y) stopped to the 2nd ord

Finding the Mach speed of an aircraft

The relationship between the cone's vertex angle, theta, and the Mach number, M, of and aircraft that is flying faster than the speed of sound is given by sin theta/2 = 1/M. If theta = Pi/2, determine the Mach speed, M, of the aircraft. Express the speed as an exact value M= Express the speed as a decimal to the neares

Real Valued function on its largest domain and Vectors

Hello, Ive got slight problems which i need to solve and understand for a entry test for a course which i hope to gain entrance into this week and im stuck on two questions on example test which i need help. see attached file can you please help me.

Solutions to Various Problems in Multivariable Calculus

Write out the chain rule for each of the following functions and justify your answer in each case using this following Theorem. Theorem: Chain Rule Let U ⊂ R^m⟶R^p and f:V⊂ R^m⟶R^p be given functions such that g maps U into V, so that f∘g is defined. Suppose g is differentiable at X_0 and f is differentiable at y_0

Factorization of Algebraic Expressions

Provide a tutorial on the factorization of algebraic expressions including: * Highest common factor * difference of two squares * sum or difference of two cubes * quadratic equations * four term grouping

Use SPSS to test effect of gender on math skills for calculus students

High School teachers were interested in the effect of gender on Math Skills in their calculus students. Analyze and graph the data below to determine if males are better at these types of skills than females. Gender F F F M F M F M M F F M F M M M Math Skills 34 40 38 30 20 40 38 47 26 24 27 37

Applied Calculus Differentiate Problems

1. Differentiate 5x-1/x / 3-ln x **in words, 5x minus 1 over x, divided by 3 minus ln x** 2. Differentiate (ln(3x) - e^2x +1)^-2 **at the end, is to the -2 power** 3. Find the price elasticity of demand at a price of $2 if D(x)=6 / 3x-1 **The price elasticity of demand is PE(P)= -p D' (p) / d(P) 4. Maximize the area

Precalculus Problems

1) One hundred stones are placed on the ground 3 feet apart, the first being 3 feet from a basket. If the basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by one? 2) 55 Freshman were interviewed about the classes they were taking this

Solving Precalculus Problems: Probability Rolling

I'm having trouble writing equations for word problems. I would like help in figuring out how to set up the right equations in order to find solutions to the following problems: 1) Marlene rides her bicycle to her friend Jonâ's house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on l