Start your trial now! First week only $4.99!*arrow_forward*

Question

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: solve the initial value problem. (x+1)dy/dx+ 2y = x, x >-1, y(0) = 1

A: Write the equation as linear differential equation.

Q: Find the volume using the shell method. x = 8y2, y ≥ 0, x = 8; about y = 2

A: Given:x = 8y2, y ≥ 0, x = 8; about y = 2

Q: Two ladders of length a lean agains opposite walls of an alley with their feet touching. One ladder ...

A: The problem can be depicted as shown below,

Q: What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral ...

A: The derivatives of the six basic hyperbolic functions are as follows.

Q: In the function: f(x)= (4x^2)/((x^2)+4) What are the critical numbers of the function? Where is t...

A: Given function

Q: Match each sequence below to statement that BEST fits it. STATEMENTS Z. The sequence converges to ze...

A: First of all, consider the method to find weather the infinite series is diverging or converging.

Q: y′=(3x2−ex)/(2y−5),y(0)

A: Click to see the answer

Q: Find the value of c so that ƒ(x) = csqrt(x)(1 - x) is a probability density function for the random ...

A: Write the given expression and simplify it using the definition of probability density function.

Q: Graph the given equation. 2x = 3

A: Click to see the answer

Q: solve the initial value problem x dy - (y + sqrt(y)) dx = 0, y(1) = 1

A: We know :

Q: How do you simplify this expression using the properties of logarithms? 11ln(8) - 11ln(1)

A: Given expression is,11 ln(8) – 11 ln(1)

Q: Derive the equation for the volume of a sphere of radius r using the shell method.

A: Consider a circle of radius (r), which when rotated around x-axis generates a sphere.

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population increase...

A: Given:At the end of 3 hours there are 10,000 bacteria.At the end of 5 hours there are 40,000 bacteri...

Q: In the function: f(x)= (9x^2)/ ((x^2)-49) Indicate the domain and range in interval notation. What...

A: Denominator of the function can not be equal to 0.

Q: Suppose that a sum S0 is invested at an annual rate of return r compounded continuously. a.Find the ...

A: Click to see the answer

Q: Physicists using the ra-dioactivity equation y = y0 e-kt call the number 1/k the mean life of a radi...

A: Given:A radioactivity equation y = y0 e-kt …(1)The mean life of a radioactive nucleus = 1/k

Q: In Exercises 5–10, find the orthogonal trajectories of the family of curves. Sketch several members ...

A: Note: We’ll answer the 5th question since we answer only one question at a time. Please submit a new...

Q: Solve the initial value problem and determine the interval in which the solution is valid.Hint: To...

A: Click to see the answer

Q: Consider the function. |r + 7|– |r – 7| f(x) = Estimate the following by evaluating fat x-values nea...

A: Given,

Q: Let h = ƒg be the product of two differentiable functions of x. a. If ƒ and g are positive, with loc...

A: a. Given information:

Q: Find the center of mass of a thin plate covering the region between the x-axis and the curve y = 2/x...

A: Click to see the answer

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and...

A: Given:Find the center of mass of a thin plate covering the region bounded below by the parabola y = ...

Q: Find the volume of the solid generated by revolving the “triangular” region bounded by the curve y =...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: What is the limit of f(x) = 3 as x approaches π? (If an answer does not exist, enter DNE.)

A: Given:

Q: y′=2y−1,y(0)=1y′=2y−1,y0=1 Hint: y1 = (1 + 2h)/2 + 1/2

A: Given,

Q: In the function: f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule...

Q: How do you find the length of the graph of a smooth function over a closed interval? Give an example...

A: known fact:

Q: Use the shell method to find the volumes of the solids generated by revolving the regions bounded by...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: A force of 200 N will stretch a garage door spring 0.8 m beyond its unstressed length. How far will ...

A: Given information:

Q: Find the volume of the solid generated by revolving about the x-axis the region bounded by y = 2 tan...

A: Given information:

Q: Find the centroid of the region bounded by the graphs of y = x + cos x and y = 0 for 0<=x<= 2p...

A: Graph is given below:

Q: Derive the formula for the volume of a right circular cone of height h and radius r using an appropr...

A: Given information:

Q: dr/dθ=r2/θ, r(1)=2

A: Click to see the answer

Q: Given the equation 5x + 2y = 4, answer the following questions. (a) Is the slope of the line describ...

A: Part (a):

Q: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at ti...

A: Click to see the answer

Q: A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/s from the roof of a building 3...

A: It is given that the mass of the ball is 0.15 kg, initial velocity 20 m/s and initial height 30 m.Th...

Q: Find the volume of the solid generated by revolving the region en-closed by the graphs of y = e^(-x2...

A: Recall the fact.

Q: Show that the area of the region in the first quadrant en-closed by the curve y = (1/a) cosh ax, the...

A: First of all, consider the graph for curve y, the coordinate axes and the vertical line x = b.The ar...

Q: How do you locate the center of mass of a thin flat plate of material? Give an example.

A: Considering that the distribution of center of mass on thin plate is uniform, so consider the co-ord...

Q: In the function: f(x)= (7x+B)/(4x+b) , with 7b>4B At which x-coordinates are there points of inf...

A: Click to see the answer

Q: How are the functions ax and log ax defined? Are there any restrictions on a? How is the graph of lo...

A: Proving that both the functions are defined. Logarithmic functions are the inverse of exponential fu...

Q: You are looking for an item in an ordered list 450,000 items long (the length of Webster’s Third New...

A: Click to see the answer

Q: Derive the formula sinh-1 x = ln (x + sqrt(x2 + 1)) for all real x. Explain in your derivation why t...

A: Define y as follows.

Q: In Exercises 31–32, find the volumes of the solids generated by revolving the regions about the give...

A: (a)Given information:

Q: find the volume . The base of the solid is the region bounded by the parabola y2 = 4x and the line x...

A: The base of the solid bounded by the parabola y^2=4x and the line x=1. And each cross section perpen...

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y ...

A: Given,

Q: Find the volume of the torus generated by revolving the circle (x - 2)2 + y2 = 1 about the y-axis.

A: To determine the volume of the torus generated by revolving the circle.

Q: Find the volume of the solid generated by revolving the region bounded by the curve x = e^y2 y = 1 a...

A: Click to see the answer

Q: Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 14 peo...

A: Let: The number of cartons of food is x cartons, x≥0The number of cartons of clothing is y ...

Q: A rock is thrown upward from a bridge that is 47 feet above a road. The rock reaches its maximum hei...

A: Click to see the answer