# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**Calculus**

I am working on a regression model , if my residuals don't exceed 0.6 does that mean this model is OK for my data?,

**Calculus**

The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? 36 sqrt 3 36 18 sqrt 3 18 The answer isn't 18 sqrt 3 for sure.

**pre calculus**

Find all of the solutions of the equation x^4-625i=0 and represent the solutions graphically.

**pre calculus**

Use the information to solve the triangle. If two solutions exist find both. 1.A=36°, B=98°, c=16 2.a=4, b=8, c=10 3.A=35°, b=8, c=12

**Calculus**

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the line y = 5.

**calculus**

your friend left his home 2 hours ago and cycles due north at 30 km/h. you have been cycling due west at 20 km/h and arrives at his home now. At what time were the two of you closest to each other?

**Calculus**

I am working on a regression model , if my residuals don't exceed 0.6 does that mean this model is OK for my data?,

**pre calculus**

find (a)2v+u, (b)u-3v), and (c)5u-v. 1.u=i-j, v=6i+9j 2.u=2i+3j, v=-i-2j

**pre calculus**

find (a)2v+u, (b)u-3v), and (c)5u-v u=<-2,-3> v=<-1,-10>

**pre calculus**

Forces with magnitudes of 250 pounds and 130pounds act on an object at angles 45degrees and -60degrees respectively with the positive axis. Find the direction and magnitude of the resultant of these forces.

**pre calculus**

Find the component form and magnitude of the vector w that has initial point(-8,-12) and terminal point (4,1)

**pre calculus**

A triangular parcel of land has borders of lengths 55 meters, 85 meters, and 100 meters. Find the area of the parcel of land.

**pre calculus**

find (a)2v+u, (b)u-3v, and (c)5u-v u=<0,-4>, v=<-2,-8>

**pre calculus**

Write the complex number 100(cos240°+ i sin240°) in standard form.

**pre calculus**

Write the complex number z=-2+2i in trigonometric form.

**AP Calculus**

I am doing the 100 meter men's freestyle swimming lab (in case you know what I am referring to) and I need to fibd the lower limit analytically. I am given a table of data containing the years after 1900 and the time in second of each country , for example: Time. Country. 55.4...

**pre calculus**

ea + bi = ea(cos b + i sin b) This formula gives rise to the equation eπi + 1 = 0. . Show how Euler’s formula can be used to derive this equation.

**pre calculus**

how do you use e^a+bi = e^(cos b + i sin b) to derive the equation eπi + 1 = 0

**calculus**

A rocket has been launched from Russia International Terminal towards the point (√tk, 〖te〗^k, k) at a speed 2000 feet/second. What is the position of the rocket after half an hour?

**Differential calculus**

reservoir has the shape of a right-circular cone. The altitude is 10 feet, and the radius of the base is 4 ft. Water is poured into the reservoir at a constant rate of 5 cubic feet per minute. How fast is the water level rising when the depth of the water is 5 feet?

**Calculus**

Find dz/dy for the following : z=(e^xy)+2ycos(xy-1)

**Differential calculus**

A ladder 20 ft long leans against a vertical wall, If top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.

**Calculus**

Determine the relative extremum for the function , f(x,y)=((x^2)+(y^2))(e^-x)

**Differential calculus**

A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.

**Differential calculus**

Find the most economical proportions for a covered box of fixed volume whose base is a rectangle with one side three times the other.

**Differential calculus**

A piece of wire of length 2 m. is cut into two parts, one of which is bent into the shape of a square and the other into a shape of a circle. How should the wire be cut so that sum of the enclosed areas is minimum.

**Calculus**

Find dz/dy for the following : xln(1-2y) = zsin((x^2)z)-3y+z

**Calculus AB**

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of x^2 - 3xy + y^2 = 1 ...

**Calculus**

The base of a triangle is decreasing at the rate of 2 cm/ min and the height is increasing at the rate of 1cm/ min. Find the rate at which the area is changing when the base is 8 cm and the height is 6 cm. Is the area increasing or decreasing at that moment?

**Calculus application of sin function**

a horizontal position of the pendulum of a grandfather clock can be modelled by h(t)=Acos(2(pi)t/T), where A is amplitude of the pendulum in meters, t is time in seconds, and T is the period of the pendulum, in seconds. If the pendulum has a velocity of v(t)=sin Pi(t) find: A...

**calculus**

Find the area of the region cut from the first quadrant by the curve r=2(2-sin2ɵ)½

**Calculus**

Find the local maximum and minimum values of the following curve within the given domain. y=SECx-TANx 0 ≤ x ≤ 2π

**Calculus - Optimization**

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 38 feet?

**Calculus applications**

A steel factory wishes to make a cylindrical container, of thin metal, to hold 100cm³, using the least possible area of metal. If the outside surface is S cm² and the radius is r cm, show that S = 2πr² + 200r-1 and hence find the required radius and height for the ...

**help me calculus**

Convert the rectangular equation to an equation in (a) cylindrical coordinates and (b) spherical coordinates. 4(x^2 + y^2) = z^2

**Calculus**

determine all asymtote(s) of f(x)= 1/(x(x-1)^2) using limits

**Calculus**

find the point(s) of inflection on the function f(x)= 10x + 10/x

**Calculus**

Find the biggest value of c that satisfy the Mean Value Theorem for integrals for f(x)= 1/(x+1)^6 on the interval [0,7]

**Calculus**

Find the average value of the function defined by f(x)= x^2 sin 3 x^3 on the interval [0, 3rd Root (pi)]

**Calculus**

An object at the origin at time t= 0 has velocity measured in meters per second, v(t) = t/30 if 0 <= t <= 90 = 3 if 90 < t <= 108 = 9-(t/30) if 180 < t When, if ever, does the object return to the origin? t=

**Calculus**

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 9xzj + exyk, C is the circle x2 + y2 = 1, z = 3.

**Calculus**

A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 2xyj + 3y2k. Find the work done.

**pre calculus**

can you please explain what steps you take to find ||u||2 when u: <-1,7> v: <6,4>?

**pre calculus**

Can you explain how to find (u • v)(u + v) when u <-1, 7> and v <4, -3>

**Calculus**

Find all values of c that satisfy the Mean Value Theorem for integrals for f(x)= x^{2} on the interval [-3, 3]

**Calculus**

If f(x) = integrate t^2 from x to x^2, then f'(x)= f'(-1)= Please help! I have no idea how to approach this.

**Calculus - fundamental theorems**

d/dx integral e^t^2 dt from 1 to x^3 Please help. I think I'm supposed to use substitution for the x^3 and then apply the chain rule but I'm not sure how to do that.

**Calculus - Fundamental Thm of Calc**

Suppose F(t) is an antiderivative of t^{3}. Then F'(t)= t^3. According to the Second Fundamental Theorem of Calculus, x ∫ (t^3)dt = ??? 1 Answer using the function F

**calculus**

how do you work out what ||u||2 is when you are given u:<-1,7> and v:<6,4>

**pre calculus**

Given: u <-1, 7> and v <4, -3> Find: (u • v)(u + v) ________________________________________ <25, 100> <-25, 100> <-75, -100> <75, -100>

**pre calculus**

Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is the projection of u onto v?

**pre calculus**

Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is ||v||2?

**pre calculus**

Use the following vectors to answer the question. u: <-1,7> v: <6,4> What is ||u||2?

**Calculus**

The radius of a conical tank is 2.7 meters and the height of the tank is 4.3 meters. Water is flowing into the tank at a constant rate of 59.5 m3/minute. At the instant the the depth of the water is 0.6 meters, answer the following: (A) At what rate is the depth of the water ...

**calculus**

Find the domain of the vector-valued function. r(t) = sin ti + 4 costj + tk plz help me working

**Calculus**

The number of people expected to have a disease in t years is given by y(t)=A•3^(t/4) i) if now year(2016) the number of people having disease is 1000, find the value of A? ii) how many people expected to have the disease in five years? iii) when are 100,000 people expected ...

**Differential calculus**

Sketch the graph of the curve y=(x-2)(x+1)(x+3)

**calculus help**

Find an equation in cylindrical coordinates for the rectangular equation. y^2 = x

**Calculus**

Evaluate ∫tan(3x)dx

**Calculus**

Evaluate ∫√(x^3+1)dx

**Calculus**

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim (tan(7x))^x x~>0

**calculus**

suppose that c(x)=3x^3 - 12x^2 +9000x is the cost of manufacturing x items. find a production level that will minimize the average cost of making x items

**calculus**

For which of the following mixtures will Ag2SO4(s) precipitate? 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.20 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.30 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) and 5.0 mL of 0.40 M AgNO3(aq) 150.0 mL of 0.10 M Na2SO4(aq) ...

**Calculus**

A small island is 2 km off shore in a large lake. A woman on the island can row her boat 10 km/h and can run at a speed of 20 km/h. If she rows to the closest point of the straight shore, she will land 6 km from a village on the shore. How far from the village should she land ...

**Calculus**

A factory is located on one bank of a straight river that is 2000 m wide. On the opposite bank but 4500 m downstream is a power station from which the factory draws its electricity. Assume that it costs $3 per meter to lay an underwater cable and $1 per meter to lay an above ...

**calculus antiderivation**

A car traveling 60 mi/h along a straight road decelerates at a constant rate of 11 ft/s2. (a) How long will it take until the speed is 45 mi/h? (b) How far will the car travel before coming to a stop?

**Calculus**

Given that x=cos^2t and y=ln(sint) find d^2y/dx^2 at the point t=π/4

**Calculus**

Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides of the box costs $1/ft2$1/ft2; the material for the base costs $2/ft2$2/ft2. Find the dimensions of the box of greatest possible volume if ...

**Math (Calculus) (mean value theorem emergency)**

Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4) such that the tangent ...

**Calculus**

An 18 meter ladder leaning against a building makes a 70 angle with ground. How far up the building does the ladder touch?

**Calculus**

Let F(x)=f(x^4) and G(x)=(f(x))^4. You also know that a^3=15, f(a)=2, f′(a)=4, f′(a^4)=12. Find F′(a) and G′(a). I don't even know where to begin.

**Pre-calculus**

prove the identity sin2x-sin2y/sin2x+sin2y=tan(x-y)/tan(x+y)

**Pre-calculus**

prove sin(x+y)+sin(x-y)/cos(x+y)+cos(x-y)=tanx

**Pre-calculus**

If sin2x=7/25, siny=-2/sq root of 13, cot y>0, and -pi/4<x<pi/4, find sin(2y-a)

**Calculus**

Consider the function g(x) = sinxcosx. a. Find an equation of the tangent line to the graph of g at (pi/3, sqrt3/4). b. Find the critical number(s) of g on the interval [0, 2pi]. Does the function have a relative minimum, relative maximum, or neither at each critical number. ...

**Calculus**

Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.) A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 68 feet per second. How high will the ball go?

**Calculus**

Integral f (x) * g (x) doesn't equal Integral f (x)dx * integral g (x)dx Why?

**Calculus**

I'm supposed to sketch a graph of two functions that have the same derivative of a graph. The graph having a horizontal line on (0,4)

**PRE-CALCULUS**

. Sam won $150,000 in the Michigan lottery and decides to invest the money for retirement in 20 years. Find the accumulated value for Sam’s retirement for each of his options: (a) a certificate of deposit paying 5.4% compounded yearly (b) a money market certificate paying 5....

**PRE-CALCULUS**

Find the accumulated value of a $5000 investment which is invested for 8 years at an interest rate of 12% compounded: (a) annually (b) semi-annually (c) quarterly (d) monthly (e) continuou

**Calculus**

Use the second fundamental theorem of calculus to find F'(x) F(x)=The integral from 0 -> x^2 (Sin(x)^2)dx

**Pre-calculus**

Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y

**Calculus**

Why are these false? If a function has derivatives from both the right and left at a point then its differentiable at that point.

**Calculus**

i need help, im not sure how to get started : 1) A piece of wire 14 m long is cut into two pieces, the length of the first piece being x m. The first piece is bent into a circle, and the other is bent into a rectangle with length twice the width. Give an expression for the ...

**calculus**

A positive multiple of 11 is good if it does not contain any even digits in its decimal representation. (a) Find the number of good integers less than 1000. (b) Determine the largest such good integer. (c) Fix b ≥ 2 an even integer. Find the number of positive integers less ...

**Calculus: Centers of Mass**

Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y^2 = 2x, and the line x + y = 4. I've graphed the function, and it looks like a triangle with one side curved (the parabola). I'm not quite sure how to go about the rest of the problem ...

**Calculus**

Approximate the area under the curve y=2/x from 1 to 2 using ten approximating rectangles of equal widths and right endpoints. Round your answer to the nearest hundredth

**re: Differential Calculus**

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^2y - siny = 0 Note: I forgot the ^2 for cos on the previous question. Sorry.

**Differential Calculus**

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^y - siny = 0

**Integral Calculus**

I am unable to find the formula for this given sequence: {2, -6/4, 24/16, -120/64, 720/256,...} So far, I know it's at least this: a(sub(n)) = ((-1)^(n+1))/(4^(n-1)) Basically, all I'm having trouble with is finding the pattern between the numerators. If anybody can help me ...

**Differential calculus**

Find the equation of the parabola w/ v(3,-4) and with directrix y=0.

**Calculus**

Find the values of c guaranteed by the mean value theorem for integrals. f(x)= x^3 [0,3]

**Calculus**

Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value.

**Calculus**

Find the value of the derivative (if it exists) of f(x) = (x+3)^(4/3) at x=-3. So I got (4*(x+3)^(1/3))/3 for the derivative and 0 for the final answer.

**Calculus**

Evaluate the definite integral (low) (high) -π/6 ∫ π/6 2sec(x)tan(x) dx

**Calculus**

How many critical points does the function f(x) = e^x - x^3 have?

**Calculus**

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 4√x [4, 9]

**Calculus**

A rectangular swimming pool is 8 m wide and 20 m long. Its bottom is a sloping plane, the depth increasing from 1 m at the shallow end to 3 m at the deep end. Water is draining out of the pool at a rate of 1 m3/min. How fast is the surface of the water falling when the depth ...

**College Calculus**

A radioactive substance has a half-life of 27 years. Find an expression for the amount of the substance at time t if 20 grams were present initially.

**Differential calculus**

Find the equation of the parabola w/ v(3,-4) and with directrix y=0.