# Calculus

**Calculus AB**

Theta is an angle between the lines L1 and L2 with the slopes m1 and m2. Prove that tan theta= (m2 - m1)/(1+m2m1).

**Calculus AB**

If r and s are roots of the pokynomial equation x^2 + bx + c, show that b=-(r+s) and c=rs

**Calculus AB**

Solve graphically (x-2)^3(x+4)(3-x)^2(x+1)^4 <0

**Calculus AB**

A hiker walks due east for 40 minutes, then changes course by going South 25 degrees West. After 20 minutes, he changes course again, this time at South 75 degrees East. He goes through this path for one hour after which he heads north reaching his final destination in 15 ...

**Calculus AB**

One of the equal angles of an isosceles triangle is 55 degrees. If the base is 20 cm, what is the perimeter and the area?

**Calculus AB**

From a height of 10 meters in the third floor of an apparent that building, the angle of depression of two cars moving on the same lane and in the same lane and in the same direction measure 29.5 degrees and 38.2 degrees. How far are the two cars from each other? This ...

**Calculus AB**

What is an algebraic expression for cot(arccos ((x+1)/2)?

**Calculus AB**

Without using a calculator, what is the exact value of sec(arctan(12/5)) - sin(arccot(3/4))

**Calculus AB**

The functions are f(x)= lnx, x>0 and g(x)=sinx. Let H be the composition of f with g, or H(x)=f(g(x)) and A) Find the domain of H B) Find the range of H C) Find the zeros of H

**Calculus AB**

If a sinusoidal function has a local maximum at (3,8) and the next local minimum at (7,-2), 1) What is the equation of a cosine function that has a graph characterized in the statement above 2) What is the equation of a sine function that has a graph characterized in the ...

**Calculus**

Calculate the interval of convergence. Sigma from n=1 to infinity of (n!*x^n)/n^n.

**Calculus AB**

If csc x = -2.5, what is the value of x?

**Calculus AB**

What are the six trigonometric functions of 2010 times pi?

**Calculus AB**

How do you solve a system of logarithmic equations? They have completely different bases: {(log(25)^3)x + (log(2)^7)y = log(5)^27 {(log(7)^8)x + (log(3)^5)y = log(49)^2

**Calculus**

divide 64 into two parts such that the product of one of them plus the cube of the other is a maximum

**Calculus**

If x^2 + y^2 = 25 and dx/dt = 8, find dy/dt when x=3.

**Calculus - Differentials**

The diameter of a shpere is measured to be 6 inches with a possible error of 0.05 inches. Use differentials to estimate the maximum error in the calculated surface area. I've gotten this far: A=4pir^2 dA=8(pi)(r)(dr) Since the problem gives me the diameter and the equation A=...

**Calculus**

A 20m ladder is leaning against a wall. Top of ladder is sliding down at 3m per second and the bottom is sliding away from the wall at 4m per second. How high is the top of the ladder and far is the bottom of the ladder from the wall.

**Calculus**

An open box is to be made from a rectangular piece of material by cutting equal squares of length x from each corner and turning up the sides. If the material is 18 inches long and 12 inches wide. What is the volume of the box as a function of x?

**calculus**

A farmer has 100 m of fencing to make a rectangular pen with 3 congruent rectangular subdivision side by side. Each subdivisions must be 3 meter wide and at least 8 meters long. What is the range of the possible length of it's division?

**Calculus**

Differentiate with respect to x 1/sin x

**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**

Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians. a. 4th quadrant b. 3rd quadrant c. 2nd quadrant d. 1st quadrant

**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 5/7ã3/2 is written in simplest form as aãb, 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 5/7ã3/2 is written in simplest form as aãb, 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**

Determine the quadrant in which a 130° angle lies. a. 4th quadrant b. 1st quadrant c. 3rd quadrant d. 2nd quadrant

**Pre Calculus**

Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians. a. 4th quadrant b. 3rd quadrant c. 2nd quadrant d. 1st quadrant

**Pre Calculus**

Determine the quadrant in which an angle, θ, lies if θ = 8π / 7 a. 3rd quadrant b. 1st quadrant c. 4th quadrant d. 2nd quadrant

**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?