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# Basic Calculus

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### Leaky Oil Can - Rate Measure

A leaky cylindrical oil can has a diameter of 4 inches and a height of 6 inches. The can is full of oil and is leaking at a rate of 2 in.^3/hr. The oil leaks into an empty conical cup with a diameter of 8 in. and a height of 8 in. A. At what rate is the depth of the oil in the conical cup rising when the oil in the cup is 3 in

### Motion under air Resistance

A shell of mass 4 kg is shot upward with an initial velocity of 500 m/s. The magnitude of the force due to air resistance is |v|/20. When will the shell reach its maximum height above the ground? What is the maximum height?

### Integrals and volume

1.see attached 2. The amount of alcohol in the bloodstream,A, declines at a rate proportional to the amount, that is dA ____= -kA. If k= 0.6 for a particular dt person, how long will it take for his alcohol concentration to decrease from 0.10% to

### Closed unit disc

Please see attachment Find the maximum of...over the closed unit disc.

### Pilot Off Course

A pilot, attempting to fly from Middletown to Westburg, a distance of 200 miles, notices after flying 180 miles that West burg is still 35 miles away because the heading was off by a few degrees. How many degrees was the heading off the desired course (to one decimal place)?

### The Closest Approach between Two Boats

Mike, who is standing on the deck of a yacht that is traveling due west at 6km/h, sees a sailboat sailing southwest at 4km/h, 3 km northwest of the yacht. How close to each other do these boats get?

### Determining Average Class Missed per Student

Mary, Pete and Michael were the only 3 students in a seminar in history. The class consisted of 15 sessions. Mary missed 1 of the classes, Pete missed 2 of the classes and Michael missed 2 of the classes. What is the average number of classes missed per student?

### Word problem with fractions

A survey of college sophomores showed that 5/6 of the males were taking a mathematics class and 3/4 of the females were taking a mathematics class. One-third of the males were enrolled in calculus, and 1/5 of the females were enrolled in calculus. If just as many males as females were surveyed then what fraction of the surveyed

### Change from cylindrical to spherical coordinates.

See attached page for problems

### Find the curl of F

See attached problem

### Critical numbers of functions

File attached

### Spherical coordinates and electrical charge

An electric charge is distributed throughout 3-space with density inversely proportional to the distance from the origin. Show that the total charge inside a sphere of radius R is proportional to R^2.

### Find a parametric representation for each of the surfaces.

Find a parametric representation for each of the surfaces. 1.) The part of the sphere x^2 + y^2 + z^2 = 4 that lies above the cone z= square root of x^2 + y^2 2.) The part of the cylinder x^2 + z^2 = 1 that lies between the planes y= -1 and y= 3

### Conservative Force

Please see attached page for problem. From a plot of F guess whether it is conservative. Then determine whether your guess is correct.

### The number of arrests y of a city over a period of time x is graphed on a rectangular coordinate system.

The number of arrests y of a city over a period of time x is graphed on a rectangular coordinate system. Write a paragraph describing your interpretation when the slope is positive, zero, and negative. If you were buying a home in this particular city, which slope would be most attractive to you and why?

### enclosed area under the polar coordinate

Find the area of the region enclosed by one loop of the curve. r = 6sin(11*theta)

### Blood pressure and weight

See attached file. The relationship between the weight of a child (w, in pounds) and the child's blood pressure (P, in millimeters of mercury) is given by the function above. a. Find the rate of change of blood pressure with respect to weight when the child's weight is 60lbs. b. Find the weight (to the nearest pound)

### The final course grade in calculus was predicted on the basis of the student's high school grade point average in mathematics

Please use any computer software to solve the problem if you want. Please provide the evidence of your work and explain your solution. Thank you.

### Metrics Elements Defined

For x an element of R upper k and y an element of R upper k define d1 (x, y) = max{|x of i - y of i| : 1&#8804;i&#8804;k} and d2 (x, y) = min{|x of i - y of i| : 1&#8804;i&#8804;k}. Determine for each of these whether it is a metric or not. Fully explain your answers. Thank you so much.

### Find the polar coordinates.

The Cartesian coordinates of a point are given. Find the polar coordinates (r,theta) of the point, where r > 0 and 0 less than or equal to theta < 2pie points are (-1, square root of 3)

### Various calculus problems

I am providing calculus problems from different sections in my book please help me understand each problem. Show all work clearly for me to learn how to work out each problem. Thank you in advance

### Taylor Approximations and Expansions

Please see the attached file for the fully formatted problems.

### Solving Extraneous Equations

Please solve below exercises using the Equation Editor. Answers are already provided for you from the actual book. You must show however how you have arrived at the answer. Section 6.5 Exercise 55 Sophomore math. A survey of college sophomores showed that of the males were taking mathematics class and of the females

### Geometry's Role in the Math

The importance of geometry's role in the math curriculum is debated in many high schools and colleges. Some schools offer the course while others have done away with it. Based on what you have learned, do you think geometry is a valuable tool for students to learn? Choose one side of this debate, state your view, support your vi

### Find the work done by a force on a given path.

Please see the attached file for the fully formatted problems.

### Converting Rectangular and Parametric Equations

Eliminate the parameter. Find a rectangular equation for the plane curve defined by the parametric equations. x = 3t, y = t + 7 y = 3x + 7 y = x/3 + 7 y = x/3 - 7 y = 3x - 7 Find a set of parametric equations for the rectangular equation: y = 2x - 2 x = t/2; y = t - 1 y = 2t; 2x = t + 2 y = 2t2 -

### Converging Subsequence

Theorem: Suppose that a sequence S of real numbers has a subsequence that converges to a real number a. Then S converges to a. I know this is true as an if and only if statement, but I need a counter example to show that just one converging subsequence isn't enough. Here are two sequences I'm considering: {1,-1,1,-1,1,-1..

### What is the period of the current?

The current I , in amperes, flowing through a particular AC circuit at time t seconds is I = 120sin(70(pi)t-pi/6) What is the period of the current? 1/35 seconds pi/120 seconds 1/420 seconds 70m seconds

### Solve the following by factoring

Please provide a step by step solution. Please see attached file.

### Connected Annulus

Prove the annulus A={z in (the set)R^2 : r <= |z| <= R} is connected. Is it sufficient to show that the annulus is homomorphic to the circle, and then since circle is connected, so is the annulus ? If so, how do you show it, if not, can you shed light on another method?