# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**calculus**

1. A rocket is fired vertically into the air. Six kilometers away, a telescope tracks the rocket. At a certain moment, the angle between the telescope and the ground is and is increasing at a rate of 0.6 radians per minute. (See the picture. I have defined y to be the height ...

**math: pre-calculus**

You have 5 grams of carbon-14; whose half-life is 5730 years. a)Write the rule of the function that gives the amount of carbon-14 remaining after x years. b)How much carbon-14 will be left after 4,000 years? c)When will there be just 1 gram left?

**math: pre-calculus**

Solve the equation. First express your answer in terms of natural logarithms (for instance, z=(2+ln5)/ln3). Then use a calculator to find an approximation for the answer. 3^x+9=2^x.

**math: pre-calculus**

If current rates of deforestation and fossil fuel consumption continue, then the amount of atmospheric carbon dioxide in parts per million (ppm) will be given by f(x)=375e^0.00609c, where c=0 corresponds to 2000. a)What is the amount of carbon dioxide in 2022? b)In what year ...

**math: pre-calculus**

Solve the equations. Log(6x-1) = Log(x+1) + log4

**math: pre-calculus**

Let u=lnx and v=lny. Write the expression ln3√x/2y in terms of u and v. For example, lnx^3y=lnx^3+lny=3lnx +lny= 3u+v.

**math: pre-calculus**

Write the expression as a single logarithm. Ln(e^3y)+ln(ey)-4

**math: pre-calculus**

Let u=ln and v=ln y. Write the expression ln(5√(x3√y)) in terms of u and v. for example, lnx^3y = lnx^3+lny = 3lnx+lny = 3u+v

**math: pre-calculus**

For the log function (h(x)=log(x+3)-8): a) Find the domain. b) Find the asymptotes. c) Find the x-intercepts.

**math: pre-calculus**

List the transformations that will change the graph of g(x)=lnx into the graph of the given function h(x)=log(x+3)-8 a) Horizontally shift the graph to the right by 3; then vertically shift downward by 8. b) Horizontally shift the graph to the left by 8; then vertically shift ...

**math: pre-calculus**

Evaluate the expression without using a calculator. Unless stated otherwise, all letters represent positive numbers. e^(ln√x+5)

**math: pre-calculus**

The Department of Commerce estimated that there were 53 million internet users in the country in 1999 and 90 million in 2002. Find an exponential function that the models the number of Internet users in year x, with x=0 corresponding to 1999.

**math: pre-calculus**

5. For the log function (h(x)=log(x+3)-8): a) Find the domain. b) Find the asymptotes. c) Find the x-intercepts.

**Calculus**

using implicit differentiation find the equation of the tangent line to the graph of the following function at the indicated point x^2 y^3 -y^2+xy-1=0 at (1,1)

**Calculus**

Water is draining from a swimming pool in such a way that the remaining volume of water after t minutes is V = 200(50 - t)^2 cubic meters. Find : (a) the average rate at which the water leaves the pool in the first 5 minutes

**calculus**

Find the limit lim x ->0 (sin^2 2x)/(x^2)

**calculus**

evaluate the definite integr 2 ∫ (x+1/x)² dx 1

**calculus**

the marginal cost function for widgets is dr/dq= 0.001Q^2+0.01Q+10 total fixed xosts equal $500 part 1= convert the marginal cost function into total cost function. part 2= determine total costs when Q=100.

**calculus**

evaluate the definite integrals 1 ∫ root(1+3x) dx 0

**calculus**

evaluate the definite integr 2 ∫ 5/(3+2x) dx 0

**calculus help amigos**

Find the point on the line 5x+5y+7=0 which is closest to the point (3,−4)

**calculus help**

integrate:dx/(3x^3-5)^3 i don,t know how to use wolframalpha plz show me step....

**differential calculus**

Beth leaves Muskegon, 30 mile north of Holland, traveling at 60 mph. Alvin leaves Holland traveling north at V=20t+40 mi/hr. When will Alvin pass Beth? How far from Holland will they be? :I think Beth's distance is d=60t-30 (using Holland as the frame of reference). Should I ...

**integral calculus**

help me integrate dx/(3x^3-5)^3 thanks

**Calculus**

Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the function and the x-axis over the given interval. f(x) = x^2 + 4x, [0, 4]

**Calculus**

Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y=4x^2 and x^2+10. Farmer Jones thinks this would be much harder than just building an enclosure...

**Calculus**

A bucket begins weighing 30 pounds, including the sand it holds. The bucket is to be lifted to the top of a 25 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.1 pounds of sand each foot it is lifted. Find the work done ...

**calculus**

calculus. suppose dR/dt= (d/R)^(2) and P(1) 4. separate the differential equation, integrate both sides

**calculus help**

integrate:dx/(3x^3-5)^3 help plz show step

**calculus help**

Integrate:(3x^5-5)^-3 dx thanks

**calculus**

find the derivative of d^2x/dt^2 if x^3=at^2 thanks

**Pre calculus**

Find the value for sin(theta), cos(2 theta)=3/4 and 270 degrees<0<360 degrees

**calculus help me plz**

integrate:dx/((x-1)sqrt(x^2-2) a tutor here direct me to a page but i do not know how to use it i tried but it did not show me any step...i need help plz

**calculus plz help me**

integrate:dx/((x-1)sqrt(x^2-2) plz show solution i plead

**Calculus**

approximate the change in the lateral surface area(excluding the area of the base of a right circular cone of fixed height of h=6m when its radius decreases from r=11m to r=10.9m S=(pi)r sqrt(r^2+h^2)

**Math**

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

**Math**

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

**Math**

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

**Math**

Consider the distribution of mathematics SAT scores of students in honors calculus at a liberal arts college. What would you expect the shape and variation of the distribution to be? A. Symmetric with little variation B. Symmetric with large variation C. Skewed right with ...

**Calculus**

Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) x=1 to 5

**Calculus**

Use the trapezoidal rule with n = 5 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) from x=1 to 5

**Calculus 3**

I need help writing the series 4 + 1/5 + .3 + 1/(3 + sqrt 2) + 1/(9+ sqrt 3) + 1/(27 + sqrt 4) + 1/(81 + sqrt 5 .... I have played with using irrational numbers, natural log and a vast variety of exponential arrangements. Any help to get me going in the right direction would ...

**calculus**

A hot air balloon is rising vertically upward from the ground. The crew of a boat from a nearby lake notices this situation and looks upward at an angle of 10 degree to see the balloon. If the boat is 400meters away from the balloon, and the angle of observation is changing at...

**Calculus**

Approximate the change in the lateral surface area(excluding the area of the base) of a right circular cone fixed height of h = 6m when its radius decreases from r=9m to r=8.9m (S=(pi)r sqrt(r^2+h^2)).

**Pre-calculus**

Consider an open-top box constructed from an 8.5 × 11 inch piece of paper by cutting out squares of equal size at the corners, then folding up the resulting flaps. Denote by x the side-length of each cut-out square. a) Draw a picture of this construction, and find a formula ...

**calculus**

rewrite each summation using the sigma notation. Do not evaluate the sums (a)3 + 4 + 5 + . . . + 93 + 94 (b)9 + 16 + 25 + 36 + . . . + 14

**calculus**

You own a small airplane that holds a maximum of 20 passengers. It costs you $100 per flight from St. Thomas to St. Croix for gas and wages plus an additional $6 per passenger for the extra gas required by the extra weight. The charge per passenger is $30 each if 10 people ...

**calculus**

Find the dimensions of the rectangle with the largest area if the base must be on the x-axis and its other two corners are on the graph of: (a) y=16-x²,-4<=x<=4 (b)x²+y²=1 (c)|x|+|y|=1 (d)y=cos(x),-pi/2<=x<=pi/2

**calculus**

Evaluate lim (1³ +2³ +3³ +…+ n3)/n^4 n →∞ by showing that the limit is a particular definite integral and evaluating that definite integral.

**calculus**

Evaluate π ∫ tan² x/3 dx 0

**calculus**

Use the Fundamental Theorem of Calculus to find G'(x) if: G(x)=∫ up(x²) bottom(1) cost dt

**calculus**

Use the Fundamental Theorem of Calculus to find G'(x) if: /x² G(x)= / cos t dt / 1

**calculus**

I'm having trouble on this question: Find the area of the region in the first quadrant that is bounded above by the curve y= sq rt x and below by the x-axis and the line y=x -2.

**Calculus**

A conical cistern is 10 ft. across the top and 12 ft. deep. If water is poured into the cistern at the rate of 1 cubic foot per second, how fast is the surface rising when the water is 8 ft. deep?

**Calculus**

A particle travels along the parabola y=ax^2+x+b. At what point do its abscissa and ordinate change at the same rate?

**Calculus**

A light hangs 15 ft. directly above a straight walk on which a man 6 ft. tall is walking. How fast is the end of the man's shadow travelling when he is walking away from the light at a rate of 3 miles per hour?

**calculus too hard help**

if y=x^x^x^x... dy/dx=? plz show working thanks got no ideal at all

**Calculus - urgent**

A lamina. defined by y>=0 with edges y=0, y=3/2(1-x^2) and x=-y+2y^2, for which the density is given by p(x,y)=y. a) define domain as union of type 1 and type 2 region. b) Calculate mass of lamina.

**calculus**

Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please

**Calculus**

A cardioid r=1+cos(theta) A circle r=3*cos(theta) a) Define the domain of the region enclosed inside both the cardioid and the circle. b) Use polar coordinates to calculate the area. (We can use symmetry about x-axis)

**Calculus**

Air expands adiabatically in accordance with the law PV^1.4=Const. If at a given time the volume is 14 cubic feet and the pressure is 40 pounds per square inch, at what rate is the pressure changing when the volume is decreasing 1 cubic foot per second?

**Calculus**

One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots. At 2 P.M. the second ship was at the place occupied by the first ship one hour before. At what time does the distance between the ships not changing?

**Calculus**

An island is 3 mi from the nearest point on a straight shoreline; that point is 6 mi from a power station. A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume ...

**Calculus**

Optimization: A man on an island 16 miles north of a straight shoreline must reach a point 30 miles east of the closet point on the shore to the island. If he can row at a speed of 3 mph and jog at a speed of 5 mph, where should he land on the shore in order to reach his ...

**calculus**

Assume that the radius ,r , of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V=43πr^3. Determine the rate at which the volume is changing with respect to time when r=5in. The volume is changing at a rate of how many in^3/min.?

**Calculus**

Find the area of the largest rectangle having one side on the x-axis and inscribed in a triangle formed by the lines y=x, y=0 and 3x+y=20.

**Calculus**

Find the area of the largest rectangle with sides parallel to the coordinate axes which can be inscribed in the area bounded by the two parabolas y=26-x^2 and y=x^2+2

**Calculus**

An object's velocity after t seconds is v(t)= 38-2t feet per second. a. How many seconds does it take for the object to come to a stop (velocity = 0)? b. How far does the car travel during that time? c. How many seconds does it take the car to travel half the distance in part...

**Calculus**

A bucket begins weighing 15 pounds, including the sand it holds. The bucket is to be lifted to the top of a 50 foot tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.1 pounds of sand each foot it is lifted. Find the work done ...

**College Algebra/pre-calculus**

The question is to evaluate each logarithm: My professor wants us to show work. Could you please tell me if I'm on the right track? Thank you!!! 1. log6^(1/36)= -2 2. ln(1/e^4)= 1/e^2 3. log7^1= 0 4. log4^64= ln64/ln4= 3 5. log10^8= ln8/ln10= .9031 6. log3^(radical 3)= I wasn'...

**Pre Calculus**

A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. ...

**Pre Calculus**

A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. a. Find a formula for the volume of the box in terms of x b. Find the value for x that will maximize the volume...

**Calculus**

Find the dimensions of the largest right circular cylinder that can be inscribed in a sphere of radius 6 inches.

**Calculus**

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.

**Math, Pre-Calculus.**

A postal airplane leaves lsland A and flies 91 miles to Island B. It drops off and picks up mail and flies 63 miles to lsland C. After unloading and loading A- mail, the plane returns to lsland A at an average rate of 300 miles per hour. How long does it take the pilot to ...

**Calculus**

Evaluate as limit approaches 0. (Without using l'hopital's rule. ( Sqrt(4+sin(x))-2 ) / (3x)

**Calculus**

find the point on the plane 5x+4y+z=12 that is nearest to (2,0,1)

**Pre-Calculus**

suppose y is directly proportional to x. if y=6 when x=4, find the constant of proportionality and write the formula for y as function of x. Use your formula to find x when y=8.

**Calculus**

Find the 4th Taylor polynomial, P4, generated by f(x) = 1/x at center a = 2 ?

**Calculus**

Sketch the region enclosed by the curves given below. Decide whether to integrate with respect to x or y. Then find the area of the region. y=4cos(x),y=4−8x/π. I thought it was the integral of 4cos(x)- the integral of 4- 8x/π on the interval 0 to π/2. This...

**pre-calculus**

Rewrite the following expression as an algebraic function of x sin(arccos(x/2)) I know sine is y, which is opposite over hypotenuse. I also know that arccos is the inverse of cosine. I'm confused on what the question is asking and what to do with the x. Please help! Thanks

**Calculus**

Find the 4th Taylor polynomial, P4, generated by f(x) = 1/x at center a = 2 ?

**Calculus**

give a parametrization of the ellipse x^2/25 + y^2/9 =1 that travels once counter clockwise in an interval at belongs to (0, 2pi)?

**calculus**

A rectangular closed box with a square base is to have a capacity of 27 cubic inches determine the least amount of material required.

**calculus**

What are the dimensions of a rectangular field of area A that requires the least amount of fencing.

**calculus**

A rectangular lot has a perimeter of 320meters determine the maximum area of the lot

**Pre-Calculus**

Determine the balance A for P dollars invested at rate R compounded N times per year for T years. Round each amount to the nearest cent P= $1000, R=3% t=10 years N=A 2=? 4=? 12=? 365=? Compounded continuously=?

**Pre-Calculus**

g(x)= x^2+7 Find the inverse of g(x) and state the domain and range for the inverse of g(x) using interval notation

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes. I want its complete solution

**Calculus**

Along reservoir has the shape of a right circular cone having a radius of 40m at the top and a height of 10m at the centre. it is being filled at a constant rate of 40 m^3/min.Find the rate at which the water level is rising when the height is 5m?

**Calculus**

A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2cm/min. At what rates are the volume and surface area of the balloon increasing when the radius is 5cm?

**Calculus 2**

Suppose that a spring has a natural length of 25 cm, and that 8 J of work is needed to stretch from a length of 50 cm to 80 cm. How far beyond its natural length will a force of 32 N keep the spring stretched? **I've tried calculating the spring constant using ...

**Calculus II**

So I'm trying to integrate a function using partial fractions. Here is the integral of interest: ∫(3x^2+5x+3)/[(x+2)(x^2+1)]dx. Since the numerator's degree of the polynomial is lesser than that of the denominator's degree, it is clear to separate. However, once I ...

**Calculus**

Sand pouring from a conveyor belt forms a conical pile the radius of which is 3/4 of the height. If the sand is filling up at a constant rate of 1/2m^3/min, at what rate is the height of the pile is growing 3 min after the pouring starts?

**Calculus II**

So I have Maclaurin series for sinx = ∑(-1)^n[x^(2n+1)]/(2n+1)!. I need to write out new series for sin(x^2). This will be equivalent to squaring the whole Maclaurin series of sinx, right? I'm just confused as to what terms are squared, and thus what the final product ...

**Calculus**

two small planes take off from the same airport at the same time. One travels north at 200 km/h, and the other, west at 150 km/h. If the planes fly at the same altitude, how fast are they separating after 2 hours?

**Calculus**

A ladder 6m long rests against the vertical wall. How far is the top of the ladder sliding down the wall when the bottom of the ladder is 4m from the wall and sliding at a speed of 1m/s?

**Calculus**

A spherical water balloon is being filled with water at the rate of 125 cubic inches per minute. At what rate is the radius increasing when the radius is 10 inches? At what rate is the surface area increasing?

**Calculus**

A bead moves on a circular wire x^2 + y^2 = 25. As it passes the point (3,4), the x-coordinate is decreasing at a rate of 2 units per second. At what rate is the y changing?

**Calculus**

A man is 2 m tall is walking at a rate of 1 m per second in a straight line away from a 10 m lamppost. How fast is the tip of his shadow moving away from the lamppost?