# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

Calculus the derivative
The height in feet of a free falling object t seconds after release is s(t)=-16t^2+ v_0t+s_0, where s_0 is the height(in feet) at which the object is realsed, and v_0 is the initial velocity (in feet per second). Suppose the coin is dropped from a height of 1454 feet. D. At ...

Calculus the derivative
Can you please check my answers and help me fix the one I don't or or did wron . The height in feet of a free falling object t seconds after release is s(t)=-16t^2+ v_0t+s_0, where s_0 is the height(in feet) at which the object is realsed, and v_0 is the initial velocity (in ...

Calculus rate of change
Can you please check my answers and fix the ones if any that are wrong. Along with help on part d Consider the following fun f(x)=(3/4)x^3- x^3-3x^2+6x A.find relative extrema and identify max and min. I got x=1 max ,±√2 min B.determine the interval(s) where f(x) is ...

Calculus rate of change
A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the base area of the base increasing? I honestly have no idea how to start this ...

Calculus
A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?

calculus
A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?

calculus
A region is bounded by y=2x and y=4sqrt(x). Find the volume when rotated along 1)y=-1 2)the y axis

Calculus
A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the tank?

pre calculus
C=2 x^=8y

Calculus
A spherical balloon is being inflated.Let r(t)=3t can represents its radius at time t seconds and let g(r)=4/3 pie r be the volume of the same balloon if its radius is r.Write (g.r) in terms of t and describe what it represents.

calculus
A door is opened by pushing inward explain in terms of torque why this is most easily accomplished when pushing at right angles to the door as far as possible from the hinge side of the door?

Calculus
How do you differentiate sin^2(cos t) My work: =2sin(cos)(cost)(-sint)

pre-calculus
Choose the point on the terminal side of -210°.

Pre Calculus
Perform the operation shown below and leave the result in trigonometric form. [8(cos10° + i sin10°)] [5(cos 200° + i sin 200°)]

Math - Studying for Pre Calc exam!
Approximate the solutions (to three decimal places) of the given equation in the interval (- pi/2, pi/2) 6 sin 2x − 8 cos x + 9 sin x = 6 Can you help with this please? I am studying for my Pre Calculus 1 exam and am stuck on this question...! The answer options are a. x...

Algebra/Calculus
If x + y = xy = 3, what is x^3 + y^3? I have tried solving this using algebra alone, but my teacher told me to use complex numbers, and I don't know how to start. Can someone please guide me to the solution to this problem? Thanks Kevin

Pre Calculus
Find the exact value ofcos (u+v) given that sin u= 7/25 and cos v=−12/13. (Both u and v are in Quadrant II.)

calculus
Find the exact value of the given expression. (tan17pi/12 - tan pi/4) / (1+tan 17pi/12 tan pi/4) can you help with this? i got the answer 1/ squareroot 3

calculus
Find the exact value of the given expression using a sum or difference formula. sin 345° Can you help with this? I got 1/4 (squareroot 2 - square root 6)

calculus
The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by S = 60.1 − 43.9 cos πt/ 6 where t is the time (in months), with t = 1 corresponding to January. Determine the months when sales exceed 7700 units...

pre calculus
Use the half-angle formula to simplify the given expression. squareroot 1+cos12x/2

Pre Calculus
Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. (sin x + cos x) ^2 a. 1+2sinxcosx b. sec^2x−tan^2x+2cosxsinx c.sec x + 2 sin x/sec x d. sin^2x+cos^2x e. 1+2cos (pi / 2 - x) cos x

Pre Calculus
Use the sum-to-product formulas to find the exact value of the given expression. sin 150° + sin 30°

Calculus
Find the critical numbers of the function f(x)=2sinx+x that lie in the interval (0,2pi)? I have the answers, but not sure how to display the work.

Calculus
Find the absolute maximum and minimum values of the function f(x)=3(x-2)^(2/3)+5 on the interval [1,10]? I'm not sure how to do this. Please help.

Pre-Calculus 11
What is the entire radial form of -3* cube root of 2? I go cube root of 54 as my answer but it is wrong

Pre Calculus

Pre Calculus
Determine two coterminal angles (one positive and one negative) for θ = −503°. a. 217°,− 323° b. 217°, − 143° c. 307°, − 413° d. 127°, − 323° e. 127°, − 233°

Pre-calculus
Equation of the parabola with the vertex (0,3), axis parallel to OX, passing through (4,9)

Pre-Calculus 11
I don't know how to solve this... Question: Suppose 5/7ã3/2 is written in simplest form as aãb, where a is a real number and b is an integer. What is the value of b? (The square root is over the whole fraction of 3/2) A 2 B 3 C 6 D 14 I think it is either A or B

Pre-Calculus 11
I don't know how to solve this... Question: Suppose 5/7ã3/2 is written in simplest form as aãb, where a is a real number and b is an integer. What is the value of b? (The square root is over the whole fraction of 3/2) A 2 B 3 C 6 D 14 I think it is either A or B

Pre Calculus

Pre Calculus

Pre Calculus

Calculus
determine the equation of a plane, P3, that intersects the planes P1: x + y + 3z − 2 = 0 and P2: x − y + 2z = 0 in a point; a line. I know the normals are (1,1,3) and (1,-1,2) clearly the lines don't intersect because the normals are't multiples. So I don't know ...

Calculus
Launching a missile to hit a target 100 miles away. Determine the launch speed of the missile along with the angle at which it's to be fired. Also, show your work and one of the angle that will work. Finally, assume that the only force acting on the missile is gravity.

AB Calculus
Assume that x, y, z and b are positive numbers. Use the properties of logarithms to write the expression logb 4(square root)x^7y^2 / z^4 in terms of the logarithms of x, y and z a. 28logbx+8logby-16logbz b. 7/4 logbx+1/2 logby-logbz c. 7/4logb(x+y-z) d. logb x+1/2 logby-logbz ...

Calculus
Evaluate the definite Integral Integral [0 to pi/4] cos(2x)sec^2(pi/4 sin(2x))dx

Calculus
use te fundamental theorem of calculus to evaluate the integral Integral [0, pi/3] sin^2(x)dx I'm confused on what F(x) should be

Calculus
A 400 N object is hanging from two ropes that are suspended from the ceiling. One of the ropes forms a 60° angle with the ceiling and has a tension of 400 N. Calculate the tension in the second rope

Pre Calculus
The population P of a culture of bacteria is described by the equation P = 1600e^0.052t where t is time, in hours, relative to the time at which the population was 1600. (a) What was the population at t = 6 hours? Show your work. (b) After how many hours will the population ...

Pre Calculus
Write the equation 5^2= 25 in logarithmic form. a. log255=2 b. log25=25 c. log52=25 d. log225=5 e. log525=2

Pre Calculus
Use a calculator to find the value for log0.94769 to four decimal places. a. –0.0536 b. –0.9767 c. 0.9767 d. 0.0232 e. –0.0232

Pre Calculus
Find the value of x. log4 65,536 = x a. x = 32,768 b. x=8 c. x = 65,536 d. x=4

Pre Calculus
16. Use a calculator to find a value for ln16.1 to four decimal places. a. 2.7788 b. –2.7788 c. –1.2068 d. 5.0814 e. 1.2068

Pre Calculus
17. population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple? a. 6 . 6 years b. 1 years c. 5 . 3 years d. 2 . 2 years e...

Pre Calculus
Assume that x, y, and b are positive numbers. Use the properties of logarithms to write the expression logb ^8xy in terms of the logarithms of x and y. a. logb^8 + logb x + logb^y b. logb^8+logbx c. logb^8+logby d. logb^8 + log8 x + log8^y e. logb^8+log8xy

Pre Calculus
Assume that x, y and a are positive numbers. Use the properties of logarithms to write the expression loga x ^6y ^7 in terms of the logarithms of x and y. a. 42loga^x+y b. 42loga^x+7loga^y c. 6loga^ x + 42loga^ y d. 6loga^x+7loga^y e. 6loga^x+6loga^y

Pre Calculus
22. Solve the equation. 2x = 5 a. x = 0.5541 b. x = 5.8628 c. x = 2.3219 d. x = 1.4307 e. x = 1.6652

Pre Calculus
Simplify the expression. log3 36 a. 6 b. 36 c. 3 d. 18 e. none of these

Pre Calculus
Simplify the expression. 9 log 9 2 This is 9 to the power of log base 9 of 2 a. 2 b. 18 c. 4 d. 9 e. none of these

Pre Calculus
Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 69 grams, how much will remain after 75 years? a. 1.5848 grams b. 61.5289 grams c. 0.0000 grams d. 1.0426 grams e. 17.2500 grams

Pre Calculus
Evaluate the function f(x) = log3 x at x =1/27 without using a calculator a. –4 b. –2 c. 1/27 d. –3 e. 27

Pre Calculus
Identify the x-intercept of the function f(x) = 2 ln(x-3). a. x=3 b. x=0 c. x=2 d. x=4 e. The function has no x-intercept

Pre Calculus
Assume that x, y, and a are positive numbers. Use the properties of logarithms to write the expression log a 9 xy in terms of the logarithms of x and y. a. 9logbx+9logby b. 19 l o g b ( x + y ) c. 19 l o g b x + l o g b y d. logbx+logby e. 19 l o g b x + 19 l o g b y

Pre-Calculus 11
Can you simplify this further? 2∛3 + 5∛3/4 - 12√11 + 5√11

Pre-Calculus 11
Simplify the following ∛375/4 This is how far I got ∛5*5*5*3/4

Pre Calculus
Can you give me an example of properties of functions in a real life example?

Pre Calculus
Write f(x) =x^3-11x^2+18x+32 in the form f(x)= (x-k) q (x) +r when k=6 + (square root)6, and demonstrate that f(k)=r

Pre Calculus
a. Identify the horizontal asymptotes of the function f(x)=x+6 / |x|+1 ( / = divided by/over) b. Make a summary of how you may sketch a graph of this rational function.

Pre Calculus
The number of new accounts opened at a credit union in the years 2001 to 2006 can be approximated by the model N(t)= -80.6t^2+2100t+12000, where 11 <= t <= 16, with t = 11 corresponding to 2001. Using this model and your graphing calculator, determine the year in which ...

Calculus
A spider is descending vertically at a rate of 0.5 cm/sec. A lizard sits patiently on the ground at a spot 15 cm feet from the shadow of the spider (assume the shadow is directly below the spider). At what rate is the spider’s angle of elevation, θ, decreasing when it ...

Calculus
Sand falls from a conveyor belt onto a conical pile at a rate of 6ft/mi^3. The radius of the base is always equal to two-thirds of the pile’s height. At what rate is the height of the pile changing when the radius of the base of the pile is 2 ft? I honestly have no idea how ...

Calculus
Sketch the graph of the function that has the following properties. f is continuous on (-infinity, infinity). points: (-1,2), (0, 0), (-1,0) f'(x)>0 at (-infinity, -1) f'(-1)=0 f'(x)<0 at (-1, 1) f'(1)=0 f'(x)>0 on (1, infinity) f"(x)<0 on (-infinity, 0) f"(0)=0 f...

calculus
the fence around a rectangular compound costs \$4 a foot for three of the four sides. the fourth side is the wall of a building, so no fence is needed for that side. we will call the distance of the fence parallel to the wall w for width and the two other sides d for depth. a) ...

Calculus
A box with square base and rectangular sides is being designed. The material for the sides costs 20 cents per square inch and that for the too and bottom costs 10 cents per square inch. The box is to hold 150 cubic inches. What dimension of the box will minimize the cost?

Calculus
A printed page is to have 1.5 inches margin on all sides. The page should contain 144 square inches of type. What dimension of the page will minimize the area while still meeting these other requirements?

Calculus
A box (with no lid) is to be constructed from a sheet of card board by cutting the squares from corners and folding up the sides. Suppose the original sheet of card board measures 16 inches by 16 inches. What would the size of the squares removed to maximize the volume of the ...

calculus
Find the volume generated by revolving about the x-axis the region bounded by the following curves y=sqrt/(4x+3),x=0,x=4, and y=0. (Use "pi" for π).

Differential Calculus
A norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window 10 m, express the area A of the window as the function of width x of the window.

Calculus
Use implicit differentiation to find the derivative of y with reapect to x x^2y-y^2+ln(xy)=1

Calculus - Discontinuity
What kind of discontinuity is this piecewise function? Removable or jump? f(x) ={ (2x^2 - 5x - 3)/(x-3) if x does not equal 3 ............6...........................​.if x = 3

Calculus
What kind of discontinuity is this: F(x)= (2x^2 - 5x -3)/(x-3) if x does not equal 3 6 if x=3 It is a pieces use function. I thought it was removable but my answer key says it is a jump discontinuity. This is from an exam review and I want to get it right.

calculus
Find the general solution of the equation. 6t*dy/dt+y=sqrt (t),t>0.

calculus
500-gallon tank initially contains 200 gallons of brine containing 100 pounds of dissolved salt. Brine containing 2 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon per...

calculus
Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the volume of the box?

calculus
What function should be used to minimize the distance between and the point (2, 0)?

calculus
Given the area of a rectangle is A = bh, and assuming the rectangle is open on one side, perimeter b + 2h = 40, what formula will maximize the area of the rectangle

calculus
a particle is moving along the curve whose equation is" y=x^2? At what point on the curve are the x and y coordinates changing at the opposite rate?

Calculus
The base of a solid is the region bounded by the lines y = 5x, y = 10, and x = 0. Answer the following. a) Find the volume if the solid has cross sections perpendicular to the y-axis that are semicircles. b) Find the volume if the solid has cross sections perpendicular to the ...

General Physics
Clarification: this is calculus-based physics, so the methodology is not restricted to trigonometry only. I have two questions, so hopefully I can divide them up nice and evenly. Also, if you know where I should copy and paste proper vector notation from, please tell me so I ...

Calculus
Related rates: The volume of a cube is increasing at the rate of 40 mm^3/s. How fast is the surface area of the cube increasing when each edge is 10 mm?

CALCULUS
State the intercepts, domain and range for y= |0.5x^2-2|.

CALCULUS
Let y(t) denote the mass of a radioactive substance at time t.t. Suppose this substance obeys the equation y′(t)=−14y(t). Assume that, initially, the mass of the substance is y(0)=M>0. At what time does half of the mass remain? (Round your answer to 3 decimal ...

Calculus
A tetrahedron is formed in the rst quadrant by the three coordinate planes and the plane that meets the x-axis at a > 0, the y-axis at b > 0 and the z-axis at c > 0. Compute its volume. Kindly help

Calculus
The position, p(t), of an object at time t is given. Find the instantaneous velocity at the indicated time c. Also determine whether it is moving forward, backward, or neither at time c. p(t)=2-1/t at c=3

Calculus
Find the area under the curve of y=-2x+6 from x=0 to x=3 using 3 strips of equal length using right endpoints. I tried this equation before and my answer was 9 but my teacher said it was wrong? and I also posted this before and Someone who helped me got the same answer. So I'm...

Calculus
Given the function 6x+3y=18, find the area under the curve from x=0 to x=3 using 3 strips of equal length using the right end points. I was working on this and so I made the equation equal to Y=mx+b form so it ends up being Y=-2x+6, and now I am completely confused.. Please ...

Calculus
lim x-->0 ((7-3x^5+x^2sinx)/(5cosx))

calculus
find the constants a and b so the function is continuous on a real line piecewise function: f(x)={5, if x<= -2; ax+b, if -2<x<3; -5, if x>=3 I know the limit x-->2- is 5 and limit x-->3+ is -5. I don't know how to find the constants

CALCULUS

Calculus
find the value of a, if it exists, such that the following function is continuous at X = 2. piecewise function f(x)={x^2-3x+1, if x>2; a, if x=2; 3-2x, if x<2 I found the limits from left and right of 2 = -1 so the limit exists but I don't know how to figure out a

Calculus
F(x)=2x^2-log(x+5)/√16+x

CALCULUS
Find the derivative of y=4sinx−2cosx

calculus
A rectangular lot is to have an area of 1600m^2. Find the shortest that can can reach the building with one end resting on the ground outside the wall

Calculus
The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given points. x 4 9 11 14 15 f(x) -6 -11 -18 -21 -25 -11...