# Calculus

**Calculus**

water drips into an upside down cone, whose diameter at the base is 10 cm , and whose height is 15 cm. If the water is dripping int a rate of 2cm^3 per minute, how fast is the height rising.

**Pre-Calculus**

Use applications of exponential functions and logarithmic functions to solve. The half-life of plutonium 241 is 14.4 years.If 100 grams is present now, How much will it take to reach 2 grams of plutonium 241? y=a(1/2)^(t/14.4) How do I solve for t? I'm not sure where to even ...

**Calculus**

Measurements of a lake’s width were taken at 15-foot intervals, as shown: x= 0 15 30 45 60 75 90 105 120 f(x)= 0 15 18 20 19 23 24 22 12 Estimate integral (0,120) f(x) dx with n = 4, using the left-hand approximation, the right hand approximation, and the trapezoidal ...

**Calculus**

I just need help with one question. A bacteria population starts with 500 bacteria and grows at a rate of r(t) = 548e^(6.5t) bacteria per hour. Determine the number of bacteria after 1 hour. Thank you!

**Calculus**

Calculate the area of the region bounded by the graphs of the given equations y=x^2-5x+4 and y=-(x-1)^2 The answer is supposed to be 9/8, but I'm getting -111/8. Idk what I'm doing wrong

**Calculus**

I need some help with this Calculus problem. A bacteria population starts with 500 bacteria and grows at a rate of r(t) = 548e^6.5t bacteria per hour. A. Determine the function P(t) which gives the population at time t. C. How long does it take the initial population to triple...

**Calculus**

Find the limit lim tan^2(7x)/9x x-> 0

**Calculus**

A rectangular box with a square base and cover is to have a volume of 2500 cubic feet. If the cost per square foot for the bottom is $2, for the top is $3, and for the sides is $1, what should the dimensions be in order to minimize the cost?

**Calculus**

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 5 (a) Find the velocity at time t. v(t) = t^2+2t-3 m/s (b) Find the distance traveled during the given time interval...

**Calculus**

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 5 (a) Find the velocity at time t. v(t) = ______ m/s (b) Find the distance traveled during the given time interval...

**Calculus**

he table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours. (10 points) a. Estimate the value of T'(8). Give units in your answer. b. What is the meaning of T'(8)? t 0 2 4 6 8 10...

**Pre-Calculus 12**

Solve using logarithm: 2^(4x+1)=3^x

**Calculus**

A piece of wire 7 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. A. How much wire should be used for the square in order to maximize the total area? B. How much wire should be used for the square in order to ...

**Calculus**

A baseball team plays in a stadium that holds 51,000 spectators. With ticket prices at $10, the average attendance had been 49,000. When ticket prices were lowered to $8, the average attendance rose to 51,000 a. Find the demand function (price p as a function of attendance x...

**Calculus**

Solve using chain rule y=(3x^3+1)(-4x^2-3)^4 So far, I have: y'=(3x^3+1)*4(-4x^2-3)^3*(-8x)+(-4x^2-3)^4*(9x^2)

**Calculus**

In a certain chemical reaction, substance A combines with substance B to form substance Y. At the start of the reaction, the quantity of A present is a grams, and the quantity of B present is b grams. Assume a<b and y≤a. At time t seconds after the start of the reaction, ...

**calculus 2**

how to find the integral of (3x+pi)cos3xdx from [pi over 6, pi over 3}

**calculus 2**

How to solve the definite integral of(3x+pi)cos3xdx from [pi over6,pi over 3]

**Calculus**

Approximate the area under the curve of f(x)=9-x^2 between x=-2 and x=3 by calculating the area of 5 rectangles for both left hand endpoints and right hand endpoints. I have the left hand and right hand endpoints, what I need help in is solving for the actual area. Thanks

**Calculus**

Find dy/dx and express the final answer with a common denominator y=ln x^(2(4x-12))

**calculus 2**

find the definite integral for 3x+pi for the fraction interval pi over 3 and pi over 6

**Calculus**

Calculate the Riemann sum of the area under the curve of f(x)=9-x^2 between x=-2 and x=3 The answer I come up with is 10/3, but when I solve using integrals, the answer I get is 100/3. Am I doing something wrong?

**Calculus**

Find dy/dx and express the final answer with a common denominator y=lnx^2(4x-12)

**Calculus**

Find y that satisfies the given condition dy/dx=20x(5x^2-1)^3; curve passes through (1,3) I took the antiderivative and ended up with 10x^2((5x^2-1)^4/4). I end up with a large number at the end, which I think might be wrong.

**Calculus**

What is the size of the smallest nonnegative angle coterminal with an angle of 1051π radians? I got 180, but it wasn't correct?

**Calculus**

Assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression giving the population of the earth at ...

**Calculus**

assuming the population of the earth changes at a rate proportional to the current population further, it is estimated that at time t=0, the earth's population was 600 million, at t=300, it's population was 2.8 billion. find an expression giving the population of the earth at ...

**World History**

Which accurately describes the contributions of Evangelista Torricelli to the Scientific Revolution? He created a sustained vacuum and discovered the principle of a barometer. He discovered calculus after his university closed due to a plague outbreak. He invented the ...

**Calculus**

Differentiate and simplify as much as possible. Cube root(5z+6/-9z+3). The answer should be y'= (23(-9z+23)^2/3)/9(3z-1)^2(5z+6)^2/3) So far, I'm stuck at y'=[23/3(5z+6)(3z+1)][((5z+6)^1/3)/((-9z+3)^1/3)]

**Math (Calculus)**

Find the length of the curve. You may use your calculator. f(x)=x^(1/3)+x^(2/3) [0,2] I understand that the function needs to be written as x in terms of y because there's a vertical tangent at x=0, but I don't understand how to go about the problem other than that.

**Calculus**

A manufacture has been selling 1050 television sets a week at $480 each. A market survey indicates that for each $25 rebate offered to a buyer, the number of sets sold will increase by 250 per week. a) Find the function representing the demand p(x), where x is the number of ...

**Calculus**

The profit function for a computer company is given by P(x)=−x^2+36x−26 where x is the number of units produced (in thousands) and the profit is in thousand of dollars. a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the ...

**calculus**

A tank of water has a base a circle of radius 2 meters and vertical sides. If water leaves the tank at a rate of 6 liters per minute, how fast is the water level falling in centimeters per hour? [1 liter is 1000 cubic centimeters]

**Calculus**

A box has rectangular sides, top and bottom. The volume of the box is 3 cubic meters. The height of the box is half the width of the base. Express the total surface area of the box in terms of the height of the box.

**Calculus**

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 20 ft, find the dimensions of the window so that the greatest possible amount of light is ...

**Calculus**

A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $9 per m2. Material for the sides costs $150 per m2. Find the dimensions of the container which will minimize cost and the ...

**Calculus**

A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $9 per m2. Material for the sides costs $150 per m2. Find the dimensions of the container which will minimize cost and the ...

**Calculus**

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 20 ft, find the dimensions of the window so that the greatest possible amount of light is ...

**Calculus**

Find the slope and y-intercept of the line through the point (6,2) that cuts off the least area from the first quadrant.

**calculus homework help stuck**

Let s(t) denote the position of a particle at time t, and let v and a be the velocity and acceleration respectively. The particle is moving according to the data a(t)=10sin(t)+3cos(t) s(0)=-4 s(2pi)=1 find a function describing position of particle s(t)=??? I do not know where...

**Calculus**

For the curve given by 4x^2 +y^2 = 48 + 2xy show that dy/dx =y-4x/y-x

**Calculus**

Find where the function is increasing and where it is decreasing f(x)=2sin(x) on [0,2pi] Thanks

**Math/calculus HELPPP**

Graph the system of inequalities, and label each with a vertex with its coordinates. y-2x≥-3 y+3>−x 3y−2x≤12 2y+x<8 I did graph this but I'm having a hard time to label each vertex with its coordinates.

**calculus**

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**Calculus**

Suppose a player is running from first to second base 20ft/s. Find rate at which distance from home plate is changing when the player is 30ft away from 2nd base?(home plate to 1st and 3rd base is 90ft)

**pre calculus- math**

$2500 is invested in an account that pays 12% interest, compounded continuously. Find the time required for the amount to triple. Round your answer to the nearest tenth of a year.

**Pre Calculus**

I have tried and tried to understand double angle identities but it just won't stick. if sin x = -0.6 and 180 (degrees) < x < 270 (degrees), find the exact value of sin 2x

**Calculus**

Suppose that f(x) and k(x) are differentiable everywhere and that f(3) = 5, f'(3) = 7, k(3) = 6, and k'(3) = 9. Find an equation of a tangent line to 3(f(x))^2 at x = 3. So the derivative of 3(f(x))^2 is 6f(x)*f'(x), and 6f(3)*f'(3) is 210. But for the tangent line, should I ...

**Hellpppp calculus**

Solve by elimination. 0.1x + 0.3y = 1.5 0.6y + 0.2x =-1.2

**Calculus**

If egg yolks have a pH of 64 then what is the pH of egg whites if they are 63 times more alkaline

**Calculus**

In a 21 meter race between a turtle and a hare, the turtle leaves 8 minutes before the hare. The hare, by running at an average speed of 0.5 meters per hour faster than the turtle, crosses the finish line 4 minutes before the turtle. What are the average speeds of the turtle ...

**Math/calculus**

Prove Sin 8theta -sin 10theta= cot 9theta (cos 10theta - cos 8 theta)

**Math/calculus**

Tan 165° Use appropriate identity and evaluate

**Math/calculus**

Cos^2x-sin^2x/sin^4x-cos^4x Simplify

**Calculus**

at what rate is the angle shown changing at that instant? x=8 y=6 z=10 dx/dt=-15 dy/dt=10 dz/dt=-6 so i tried it by doing sin(0)=y/z (d0/dt)cos(0)=(dy/dt)/(dz/dt) (d0/dt)(8/10)=(-10/6) (d0/dt)=-25/12 rad/hour did i miss it because i didn't do the quotent rule?

**Math/calculus**

Graph f (x) = 3cos (4pix -pi/2) -2

**Math/calculus**

Earth orbits the sun at an average distance of about 150 million kilometres every 365.2564 mean solar days, or one sidereal year. What is the linear velocity of th3 Earth in kilometres per hour?

**Math/calculus**

A small plane leaves Victoria airport and flies at a compass heading of 330°. If the plane cruises at 125km/he for 90mins, how far north and how far west will the plane gave flown

**Calculus**

Find the inflection points y=x^2/x^+3 So far I've found y'=6x/(x^2+3)^2 but I'm stuck in finding y''. So far, I'm at 6(x^2+3)^2-24(x^2+3)/(x^2+3)^4 and the next step says y''=6(-3x^2+3)/(x^2+3)^3=0 and I don't understand how. Thanks

**Calculus**

Find the extreme values of the function and determine the intervals where the function is increasing/decreasing expressed in interval notation. x(x-2)^2 So far I've found y'=3x^2-8x+4. Thanks

**Calculus**

A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle.

**Calculus 2**

Find the volume of the solid generated by revolving the region bounded by the graphs of the quations about the x-axis. Y=x^2+4 Y=-x^2+2x+8 X=0 X=3

**Calculus**

Which value of c satisfies the MVT for f(x) = x*sinx on [1,4]? My answer is 2.463.

**Pre-Calculus**

Umm, how do I find this? with work? Use a calculator to evaluate the function at the indicated value of x. Round your answer to four decimal places. f(x) = 3 ln x x = 0.32

**Calculus 1**

A kite 100 ft above the ground moves horizontally at a speed of 9 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out?

**calculus 1**

Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) 6 cos(x) = x + 1 can somebody explain to me step by step on how to solve this problem?

**Pre-Calculus 12**

How do I solve the following question: sin(5x)cos(3x) - cos(5x)sin(3x) = 1 So far I got this: sin (8x) = 1 Please help

**Calculus**

Let f(x)=sqrt(x+2) and use the Linear Approximation to this function at a=14 with Δx=0.3 to estimate f(14.3)−f(14)=Δf≈df=

**Calculus**

Use a Linear Approximation to estimate sin(64∘)−sin(60∘)≈

**Calculus**

A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.8m^3/min. How fast is the water level rising when it is 2.7 m?

**calculus 1**

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x → 0 (x 6x)/(6x − 1)

**Calculus AB/BC**

What's the purpose of finding derivatives? I don't understand why you would need to find a derivative, which is the tangent of the slope of a point on a graph, to find something like "How far did Bob fall". Confusing. Please help. Thank you!

**Calculus**

f(x) = sqrt(x+1) a=3 change of x =.8 to estimate f(3.8)-f(3) use linear approximation

**Calculus**

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV1.4=C where C is a constant. Suppose that at a certain instant the volume is 610 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate ...

**Calculus**

A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π5 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at...

**Calculus**

A car travels down a highway at 45 m/s. An observer stands 250 m from the highway. a) How fast is the distance from the observer to the car increasing when the car passes in front of the observer? (b) How fast is the distance increasing 30 s later?

**Calculus**

A man of height 1.4 meters walk away from a 5-meter lamppost at a speed of 2.9 m/s. Find the rate at which his shadow is increasing in length.

**Calculus**

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 7 m from the dock?

**Calculus**

A 18 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 2ft/sec. Find the velocity of the top of the ladder at time t=2

**Calculus**

A balloon rises vertically at a rate of 8 feet/sec. A bird flies 40 feet above ground toward the balloon’s path at 20 feet per second. At what rate is the distance between the bird and the balloon changing when the bird is 50 feet from the balloon (straight line distance) ...

**Calculus**

If there is a critical point between intervals where a function is increasing on both intervals, is there a relative max/min at that point?

**Calculus**

Find the intervals on which x^2/(x-3)^2 is decreasing. a. (0,6) b. (0,3), (3,6) c. (-inf,0), (6,inf) The critical numbers are x=0 and 6, but since there is an asymptote at x=3, I'm not sure whether a or b is the answer.

**Calculus: Optimization**

A person on a lake in a canoe 1 mile from the nearest point "P" on a straight shore line; the person wishes to get to a point "Q" , 10 miles along the shore from "P". To do so, the canoe moves to a point "R" between P and Q and then walks the remaining distance to"Q". The ...

**Pre-Calculus**

Solve the equation on the interval [0,2pi). 2sin^2x-3sinx+1=0 (2sinx+1)(sinx+1) I don't think I did the factoring correctly. When I multiply it out to double check I get 2sin^2x+3sinx+1

**Calculus**

Consider the area between the graphs x+2y=4 and x+4=y2. This area can be computed in two different ways using integrals 1) Compute as a sum of two integrals 2) Compute as a single integral 3) Either way, what is the area? __ So for 1) I rewrote the two to be: x = 4-2y x = y^2-...

**calculus 1**

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 4x3 + x2 + 4x

**calculus**

One ship is sailing South at the rate of 5 knots, and another is sailing East at a rate of 10 knots. At 2 p.m the second ship was at the place occupied by the first ship one hour before. At what time was the distance between the ships not changing?

**Calculus**

Find dy/dx for y=3tan^-1(x/2). I know the answer is 6/x^2+4 but I'm stuck at y'=3(1/1+(x/2)^2)(1/2)

**Calculus**

A piece of ice stays in the shape of a sphere as it melts. The volume of the ice is decreasing at a constant rate of 3π/2 cubic feet per hour. What is the rate of change of the surface area of the piece of ice when the radius is 10 feet? I found the rate of change of the ...

**Math Calculus**

Sketch the graph of a function having the following features: f'(x)>0 on (-5,-2) and on (3,oo) f'(x)<0 on (-oo,-5) and on (-2,3) f''(x)>0 on (-oo,-3) and on (1,oo) f''(x)<0 on (-3,1) Please help!

**calculus**

A water trough is 8m long and its cross-section is an isosceles triangle which is 60cm wide at the top, and the height is 60cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm^3, when the depth of the water is d cm. Thank you in advance!!

**Calculus 1**

At 2:00 pm a car's speedomoter reads 20 mph, and at 2:10 pm it reads 25 mph. Use the Mean Value Theorem to find an acceleration the car must achieve.

**Calculus II**

Hi, I can't seem to find out how to do this. My textbook has two Q(t) values in the example and I don't know how to interpret this problem. An institute finds that the average student taking Elementary Machine Shorthand will progress at a rate given by dQ/dt = k(85 − Q) in a...

**BC Calculus**

Fluid is flowing in a tube that has a radius of 3 centimeters. Water is flowing through a circular cross section at a rate of (9-r^2) cm/s, where r is the distance from the center of the cross section. What is the total amount of water that flows through the cross section in 4...

**Calculus**

describe the transformations that produce the graph of g(x)=1/2(x-4)^3+5 from the graph of the parent function f(x)=x^3 give the order in which they must be preformed to obtain the correct graph pls help!!!

**pre calculus**

Double Angle Formula. If the double angle formula for cos2(u) = 2cos^2(u)-1, then write the double angle formula for cos2(u) in terms of sine.

**pre calculus**

how long will it take for an investment to triple if it is compounded continuously at 4.2%

**calculus**

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

**Calculus**

Suppose the height of an object fired straight up from the level ground is given by s(t)=300t-4.9t where s is measured in meters and t is measured in seconds. how fast is the object moving up as it leaves the ground after 2 seconds? find the average velocity on the interval [1...

**Calculus**

a pebble is dropped into a calm pond, causing ripples in the form of concentric circles. the radius r of the outer ripple is increasing at a constant rate of 1 root per second. When the radius is 4 feet, at what rate is the total area A of a disturbed water changing? Thank you!