# Calculus

deferential calculus
a woman is walking at the rate of 5 feet per second along the diameter of a circular courtyard. a light at one end of a diameter perpendicular to her path casts a shadow on the circular wall. how fast is the shadow moving along the wall when the distance from the woman to the ...

Integral Calculus
We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer from part (a) and the power series to find a...

Calculus
A ballast is dropped from a stationary hotair balloon that is hovering at an altitude of 500 ft. The velocity of the ballast after t sec is -32t ft/sec. a) Find the height h(t) of the ballast from the ground at time t. Hint: h'(t) = -32t and h(0) = 500. h(t) = 500 - 16t^2 ft. ...

Calculus
Let F(x) = 0∫x e^(t^2)dt a) Compute limx → ∞ (xF(x))/ (e^(x^2)) b) Compute limx → 0 F(x)/(xe^(x^2))

Calculus
Let F(x) = 0∫x e^(t^2)dt a) Compute limx → ∞ (xF(x))/ (e^(x^2)) b) Compute limx → 0 F(x)/(xe^(x^2))

calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, state whether the graph of g has a local ...

Calculus 1
If each edge of a cube is increasing at the constant rate of 4 cm/s. How fast is the volume of the cube increasing when the length x of an edge is 11 cm long?

Calculus
Find all values of c that satisfy the Mean Value Theorem for f(x) = x^3 + 1 on [2, 4].

Pre-Calculus
Convert to rectangular: theta=2pi/3

Math -Calculus
Hi, I need help with the problem: "Use a definite integral to find the area of the region under the curve y=6-4x^2 and above the x-axis". I keep getting stuck at 6x-(4x^3/3). Thanks!!

Pre-Calculus
Which are examples of the use of parametric equations? A. Position of a person on a ferris wheel. B. Position of a ball after being thrown. C. A and B D. Neither A nor B

Pre-Calculus
Which is the best example of the use of parametric equations? A. Measuring weight on the moon. B. Finding the position of a person in a city. C. Determining the position of a satellite during a specific time of day. D. Finding the right parameters to use for a construction ...

Calculus
For which pair of functions f(x) and g(x) below will the lim(x->infinity) f(x)g(x)≠0 a)f(x) = 10x + e^-x; g(x) = (1/5x) b)f(x) = x^2; g(x) = e^-4x c)f(x) = (Lnx)^3; g(x) = 1/x d)f(x) = √x; g(x) = e^-x

Calculus
If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that a)f'(c)=3 b)f'(c)=0 C)f(c)=-15 d)f(c)=3 I understand that you are supposed to use the mean value theorem, but i dont ...

pre calculus
can you check this question? An object moving vertically is at the given heights at the specified times. Find the position equation s = at^2 + v0t + s0 for the object given the following conditions. •At t = 1 seconds, s = 48 feet •At t = 2 seconds, s = 64 feet •At t = 3 ...

Calculus 1
Water is flowing into a vertical cylindrical tank of diameter 4 m at the rate of 2 m3/min. Find the rate at which the depth of the water is rising. (Round your answer to three decimal places.)

Calculus 1
If each edge of a cube is increasing at the constant rate of 4 cm/s. How fast is the volume of the cube increasing when the length x of an edge is 11 cm long?

Calculus MATH
Problem statement a) Suppose f(x) is defined on 0 ≤ x ≤ 1 by the following rule: f(x) is the first digit in the decimal expansion for x. For example, f(1/2) = 5 and f(0.719) = 7. Sketch the graph of y = f(x) on the unit interval with appropriate scales for x and for y. Use...

Calculus
Consider the function f(x) = {0, x = 0 and 1 - x, 0 <= x <= 1}. Which of the following statements is false? a. f is differentiable on (0, 1). b. f(0) = f(1) c. f is continuous on [0,1] d. The derivative of f is never equal to zero on the interval (0,1). B and D are true...

Calculus AB
Please help me with this WS 1) Find the value of lim as x-->-(square root of 3) of (-x^4 + 5x^2 -6)/(x+(square root of 3) 2) Find the distance between the discontinuities of g(x)= ((square root of x-4))/(x^2 -5x -1) 3)Find the value of x at which the curve y=(x^2 - 4)/(x^5...

Calculus
Which of the following functions does not satisfy the conditions of the Mean Value Theorem on the interval [-1, 1]? a. 5th root of x b. 2x arccosx c. x/(x - 3) d. sqrt(x + 1)

Integral Calculus
Volume of the area bounded by y=sin(x), x-axis, x is greater than or equal to 0 but less than or equal to pi, revolved about x=3pi/2.

pre calculus
Use Gaussian elimination to write the system of equations given below in row-echelon form. 2x+4y+z=-4 2x-4y+6z=13 4x-2y+z=6

Calculus
For what values of the constants a and b is (1,3) a point of inflection of the curve y=ax^3+bx^2?

Calculus
a projectile is fired vertically upward from ground level with a velocity of 1600 ft/sec. If air resistance is neglected, find its distance s(t) above ground at time t. What is its maximum height?

pre-calculus
A.) A Ferris wheel has a radius of 32 feet and completes one revolution every 5.4 minutes. What is the speed of the Ferris wheel (in radians per minute)? _______radians per minute B.) A Ferris wheel has a radius of 39 feet and travels 5.6 feet every second. What is the speed ...

pre calculus
Use Gaussian elimination to write the system of equations given below in row-echelon form 2x+4y+z=-4 2x-4y+6z=13 4x-2y+z=6

Pre-Calculus
Can you please give and example of a hyperbola and ellipse with the same vertices and center that I can graph? Then explain the similarities and differences between the graphs.

Pre-Calculus
given: ((x-2)^2/9)+((y-4^2/16)=1 what is the major axis?

pre calculus
solve 2x + y = 8 4x + 2y = 16

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

pre calculus
Create systems of equations in two variables that have (a) no solution, (b) one distinct solution, and (c) infinite solutions. Show that each system has the indicated number of solutions by using a graph or solving the system.

pre calculus
Describe the advantages and disadvantages of The method of substitution”, “The method of graphing”, and “The method of elimination” of solving systems of equations

Calculus
A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 5cos(t) − sin(3t), measured in feet. What is the acceleration of the particle at time t = π seconds?

Calculus
The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 1 ≤ t ≤ e? a)1 b)e c)e-1 d)1/(e-1)

Calculus
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t^2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop? a)60 sec b)40 sec c)20 sec...

Calculus
A particle moves with velocity function v(t) = 2t^2 − 3t − 3, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 2 seconds. a)3/4 feet per second^2 b)-1 feet per second^2 c)32 feet per second^2 d)5 feet per second^2

Calculus
A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t)=(t)In(2t). Find the acceleration of the particle when the velocity is first zero. a)2e^2 b)2e c)e d)None of these Any help is greatly appreciated

Math (Calculus) (Related Rates)
A boat pulls away from a dock at 2 m/s, but the operator has neglected to remove the tow rope used to pull the boat up to the dock. This rope runs thru a pulley which is attached to the dock at a point 1 m higher than the point at which the rope is attached to the boat. A) How...

Math (Calculus) (Related Rates)
A boat pulls away from a dock at 2 m/s, but the operator has neglected to remove the tow rope used to pull the boat up to the dock. This rope runs thru a pulley which is attached to the dock at a point 1 m higher than the point at which the rope is attached to the boat. A) How...

calculus need help studying now
find the point of coordinates of the point of inflexion on the curves (a):y=(x-2)²(x-7) (b) y=4x^3+3x²-18x-9 plz i tried my best and i got(11/6, -31/216) but keep saying am wrong

pre calculus
A small fast food restaurant invests \$4000 to produce a new food item that will sell for \$3.50. Each item can be produced for \$2.15. How many items must be sold in order to break even? Round to the nearest item.

Math (calculus) (optimization)
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder must have a volume of 4000 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize cost. I got as far as ...

pre calculus
Find all of the solutions of the equation x4-625i=0 and represent the solutions graphically. what is the next step to answer the question? (x^2-25√i)(x^2+25√i) (x-5∜i)(x+5∜i)(x-5∜i i)(x+5∜i i) i = 1 cis π/2 ∜i = ∜1 cis π/8

pre calculus
How do you use de Moivre's formulas to find ∜i?

Math (calculus) (mean values)
A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months. s(t)=155(7-9/(2+t)) a) Find the average rate of change of s(t) during the first year. Which my answer was 1395/28 b) During what month of the ...

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 ...