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
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).
1. Evaluate the following inde finite integrals: 1. 1/x^2 dx 2. e^(-x) dx 3. sin(t) cos(t)dt 4. sqrt(s) ds 2. On a dark night in 1915, a German zeppelin bomber drifts menacingly over London. The men on the gro
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.
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
Consider the following University Database schemas: Department (D-code, D-Name, Chair-SSn) Course (D-code, C-no, Title, Units) Prereq (D-code, C-no, P-code, P-no) Class (Class-no, D-code, C-no, Instructor-SSn) Faculty (Ssn, F-Name, D-Code, Rank) Student (Ssn, S-Name, Major, Status) Enrollment (Class-no, Student-Ssn) Tran
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.
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
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.
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.
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,
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
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.
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
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?
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,
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
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?
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
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
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).
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 <!--[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
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
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
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
Please see the attachment for the problems.
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.
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