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# Basic Calculus

### Bearings for the laps in a boat racing.

A boat race runs along a triangular course marked by buoys A, B, and C. The race starts with the boats headed west for 3600 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1500 meters and 2800 meters. Draw a diagram that visually represents the problem, and find the bearings fo

### Lobster boat is situated due west of a lighthouse

A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat. From the barge the bearing to the lighthouse is 63 degrees (12 km is the length of the side adjacent to the 63 degree bearing). How far is the lobster boat from the light house?

### Angular Displacement

The flywheel of a gasoline engine rotates at an angular speed of 3240 rpm. Find its angular displacement (in revolution) in 10 sec.

### Transportation Cost

For speeds between 40 and 65 mph, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 2.23 per gallon, and the driver is paid 15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck.

### Find the value of a cotangent.

Find the value of cot 35.2 degree rounded to four significant digits.

### Buoyancy and Terminal Velocity

Archimedes principal of buoancy states that an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid the object displaces. A rectangular box 1foot X 2 feet X 3 feet and weighing 384 lbs. is dropped into a 100 foot deep freshwater lake (density 62.4 lbs/cubic foot). The box immediately begins to

### Simplifying Polynomials - Showing all Steps

See attached file for full problem description. Can you show more steps in the problems how you got the answer?

### Velocity, Time and Displacement

A stone is dropped from a high cliff and falls with velocity v = 32t feet per second. How many feet does the stone travel during the first 3 seconds?

### Using Rectangles to Approximate Area

Use rectangles to approximate the area bounded by the graph of the function f(x) = x3, the x-axis, and the lines x = 0 and x = 2. Use n = 4 subintervals.

### Width of Subintervals

If we break the interval from x = -1 to x = 1 into n = 4 subintervals, what is the width of each subinterval?

### Interpolation - Lagrange's Interpolation

Calculus engineering math, Lagranges Interpolation, Quadratic Interpolation, Interpolating polynomial. See attached file for full problem description.

Please show steps on how you get the answer, type out if possible for easy reading. (See attached file for full problem description)

### Suppose a Satellite Travels at a Speed of 12560 mph

Suppose a satellite travels at a speed of 12560 mph about a planet having planetary radius equal to 4000 miles. assuming the satellite makes one full revolution about the planet every 3 hours, find the height of the satellite.

### Velocity and Displacement

A toy rocket shot straight up from the ground and travels so that its distance from the ground after t seconds is s(t) = 150t - 16t2 What is the velocity of the rocket after 2 seconds have passed? See the attached file.

### Interest and Finding the Equation of an Ellipse

1. An ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse. 2. One

### Temperature of a Thermometer

The temperature of a thermometer that is x inches from a fire is given by (see attached). T(x) = ___840_ 1 + 0.5x degrees What is lim T(x) x&#61614;0+

### Primitive Roots Determined

Determine which elements of Z_7 (Z sub 7) are primitive roots.

### Why the Condition is Placed at the End of the Formula

An open container is such that each horizontal cross section is an equilateral triangle. its base has side of a length 10cm and its top has sides length 10x cm. each sloping edge has length 20cm. the surface of the container is modelled by part of an inverted triangular pyramid. the capacity V(x) litres is : V(x)=1/12 (x^2

### Equilibrium demand and price

Find the equilibrium demand. Find the equilibrium price (in dollars). supply: p = 2000 / 2000-q supply: p = 7000 - 3q / 2q 2000/2000-q = 7000 - 3q / 2q => (See attached file for full problem description)

### Verify each equation is an identity

Verify each equation is an identity (double angle used in this chapter). See attached file for full problem description.

### Integral calculus

(See attached file for full problem description) Use integral calculus to solve differential equation problems...

### Integrate Functions and Use Calculus to Solve

Calculus: Integrate functions and use calculus to solve problems. 1. Find the following integrals a) e^5x dx b) cos x sin 5x dx c) (3x + 4)/(x + 3) dx d) (2x + 5)/(x^2 + 5x) dx 2. The diagram shows the shape of a metal component required in a manufacturing process. The area of the flat metal component is descr

### finding area of region, total cost function, midpoint rule

Any help would be appreciated on finding area of region, total cost function, midpoint rule. marginal cost. (See attached file for full problem description) --- A. Find the area of the region bounded by y=1/x and 2x + 2y=5 B. Find the area of the region bounded by the graphs of y= -x^2 + 2x and y=0 C. Find y=f

### Concentration, Rate of Flow and Dilution

In a tank containing 100 gallons of fresh water, 10 lbs of salt was added instead of 20 lbs. To correct the mistake, fresh water was added at the rate of 3 gallons per minute while draining off the well stirred salt solution from the tank at the same rate. How long will it take until the tank contains the correct amount of salt?

### Solutions of Newtonian Viscous Flow Equations

3-34. A sphere of specific gravity 7.8 is dropped into oil of specific gravity 0.88 and viscosity = 0.15 Pa s. Estimate the terminal velocity of the sphere if ts diameter is (a) 0.1 mm, (b) 1 mm, and (c) 10 mm. Which of these is a creeping motion?

### Soliving Integrals Using Ratios of Polynomials

Please see the attached file for the fully formatted problems. Please redo showing all steps.

### Factorizing Quadratic Equations and Finding the Vertex of a Parabola

Solve these quadratic equations by factoring 1. x2-4x+5 = 1 2. x2-10= -9 3. x2+8x+16 = 0 Quadratic graphs: Locate vertex and 1 point on the left hand side and 1 point on the right hand side of the vertex for the following quadratic functions 4. y = x2-2x+1 5. y = x2-1

### Given velocity and distance, please find the minimum time.

From a raft 50m offshore, a lifeguard wants to swim to shore and run to a snack bar 100m down the beach. a. if the lifeguard swims at 1m/s and runs at 3m/s, express the total swimming and running time t as a function of the distance b. find the minimum time

### Calculus Word Problems : Equation of an Ellipse, Interest Rate and Lotto Combinations

Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways. An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse.

### Short Calculus Problem for Resistance

**See attached word document*** The total resistance, R, of a particular group is given by the formula: This formula can be simplified to the form where A and B contain no fractions. Please show how to re-write with no fractions and how you arrived at the new equation...