Friday
February 27, 2015

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

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Pre-calculus (Trigonometry)
The rotating spotlight from the Coast Guard ship can illuminate up to a distance of 250 m. An observer on the shore is 500 m from the ship. HIs line of sight to the ship makes an angle of 20 degrees with the shoreline. What length of shoreline is illuminated by the spotlight...
Friday, February 27, 2015 at 2:02pm

calculus
limx¨0 sin ^3 (3x)/ x sin(x ^2)
Friday, February 27, 2015 at 4:11am

Calculus
Find an equation of the normal line to the parabola y=x^2−8x+1 that is parallel to the line x−6y =7.
Thursday, February 26, 2015 at 7:04pm

Calculus II
A square plate of side 3 m is submerged in water at an incline of 30 degrees with the horizontal. Calculate the fluid force on one side of the plate if the top of the plate lies at a depth of 6 m. (* The only thing i can think to use is the equation: p * g * (S from a to b of...
Thursday, February 26, 2015 at 5:25pm

linear algebra
Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector space, which is denoted by C(−&#...
Thursday, February 26, 2015 at 4:20pm

Calculus
Differentiate the function. y = e^(x+2)+8 y'=?
Thursday, February 26, 2015 at 1:57pm

Calculus
Find an equation of the tangent line to the curve at the given point. y =x^4+4x^2−x,(1,4) y=?
Thursday, February 26, 2015 at 1:51pm

Calculus
Differentiate the function. g(u) = sqrt(2)u+sqrt(7u) g'(u)=?
Thursday, February 26, 2015 at 1:50pm

math
let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ¨’ g by (f ¨’ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector space, which is denoted by C(&#...
Thursday, February 26, 2015 at 11:30am

calculus
Salmonella bacteria, found on almost all chicken and eggs,grow rapidly in a nice warm place. If just a few hundredbacteria are left on the cutting board when a chicken is cut up,and they get into a potato salad, the population beginscompounding. suppose the number present in ...
Thursday, February 26, 2015 at 7:33am

Calculus
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to use the washer method but I can't figure out...
Thursday, February 26, 2015 at 12:43am

Calculus Chain rule
y = (6x^2-6)^4/x I would appreciate it more if work was shown. Thank you (I have the answer but want to know how to do it)
Wednesday, February 25, 2015 at 8:32pm

Calculus 2 II
integral from 0 to 1 of x-4/(x^2-5x+6) I do believe we can integrate with partial fractions, and I should factor it in order to create a linear case 1 thingy so then, it will be: x-4/(x-2)(x-3) After that, I will find the value of a/(x-2) + b/(x-3). But I suck at matrices but ...
Wednesday, February 25, 2015 at 5:02pm

calculus
Describe three situations in which you may want to know the projection of one vector onto another.
Wednesday, February 25, 2015 at 1:41pm

College Math (Calculus)
Suppose the length of a rectangular box, with lengths x,y,z are changing at the following rates dx/dt = 2 cm /sec dy/dt = -3 cm /sec dz/dt = 1 cm/ sec when x =4, y=3 z=2, Find i) Rate at which volume is changing wrt time, ii) Rate at which the diagonal length of the box is ...
Wednesday, February 25, 2015 at 11:00am

Calculus
1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). 4. Find the derivative of 2^(e^(sin x)). ...
Tuesday, February 24, 2015 at 11:46pm

Pre-Calculus(Trigonometry)
An 8-m boom is used to move a bundle of piping from point A to point B. Determine the exact vertical displacement of the of the boom when the operator moves it form 30 degrees to 60 degrees. (Just need work checked) --------------------------------------- I drew two triangles ...
Tuesday, February 24, 2015 at 10:42pm

Pre-Calculus ( Trigonometry)
The point P(k, 24) is 25 units from the origin. If P lies on the terminal arm of an angle, theta, in standard position, 0 < theta < 360,determine the measure of theta. Unsure how to go on from here. I'd appreciate if someone can guide me through the first few steps ...
Tuesday, February 24, 2015 at 8:54pm

Calculus
Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the center of mass lie at its midpoint, to the left, ...
Tuesday, February 24, 2015 at 10:37am

business math
A local Barnes and Noble paid a $79.44 net price for each calculus textbook. The publisher offered a 20% trade discount. What was the publisher’s list price?
Tuesday, February 24, 2015 at 6:43am

[Calculus] U-substitution for Integrals
Integral of cos(x)*a^sin(x) + C dx = Integral of cos(x)*sin(x)^a + C dx = Let a be a fixed positive number. I'm clueless is to how to solve for a...
Monday, February 23, 2015 at 8:40pm

[Calculus] U-substitution for Integrals
Integrate from 1 to 5 of (3x-5)^5 dx = Integrate from a to b of f(u) du where (I have solved this part) u = 3x-5 du = 3 a = 0 b = 12 The original value of the integral is 165888 via calculator here's my last question, and it has to be in terms of u: f(u) = ? (Again, in ...
Monday, February 23, 2015 at 7:23pm

Calculus 2
Consider a trough with triangular ends where the tank is 10 feet long, top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3, and pump is used to empty the tank until the water ...
Monday, February 23, 2015 at 6:58pm

Calculus 2
Let a thing rod of length a have a density distribution function p(x)+10e^(-.1x), where x is measured in cm and p in grams per centimeter. A) if the mass of the rod is 30 g, what is the value of a? B) For the 30g rod, will the center of mass lie at its midpoint, to the left, ...
Monday, February 23, 2015 at 6:55pm

calculus
State whether or not the following statements are true. Justify your reasoning.? a. Vector a • (Vector b + Vector c) = Vector a • Vector b + Vector a • Vector c b. Vector a × (Vector b + Vector c) = Vector a × Vector b + Vector a × Vector c c. ...
Monday, February 23, 2015 at 2:01pm

Pre-Calculus (Trigonometry)
An angle in standard position such that sinÈ = 5/13. Determine the possible values of È, to the nearest degree. Answer: I got 23°. (How do I get the second one?)
Sunday, February 22, 2015 at 9:40pm

calculus
given the velocity of a particle traveling along the y-axis by v(t)=tsin(t^2)
Sunday, February 22, 2015 at 9:08pm

Calculus
When given the f graph, how do you determine extrema of F(x)? Concavity of F(x)?
Sunday, February 22, 2015 at 6:42pm

calculus
Find the integral of (sin^5 x)(cos^5 x)
Sunday, February 22, 2015 at 2:26pm

calculus
A woman is attached to a bungee cord from a bridge that is 38m above a river. Her height in meters above the river t seconds after the jump is y(t)=19(1 + e^-1xcos(t)) for t>0. What is her velocity at t=1 and t=4?
Saturday, February 21, 2015 at 8:47pm

Calculus
Evaluate: the integral from pi/8 to pi/6 csc2xcot2xdx
Saturday, February 21, 2015 at 6:56pm

Calculus
Evaluate by U-substitution: the integral of xcubedroot(x-2) dx
Saturday, February 21, 2015 at 6:55pm

Calculus
A spring has a natural length of 18 cm. If a 22-N force is required to keep it stretched to a length of 24 cm, how much work W is required to stretch it from 18 cm to 21 cm? (Round your answer to two decimal places.) Arg, another question that has me stumped! Would love some ...
Friday, February 20, 2015 at 5:10pm

Calculus
If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring? Any help would be appreciated!
Friday, February 20, 2015 at 5:09pm

AP calculus
If 54 J of work are needed to stretch a spring from 15 cm to 21 cm and 90 J are needed to stretch it from 21 cm to 27 cm, what is the natural length of the spring?
Friday, February 20, 2015 at 2:11pm

Calculus Physics
A 1559-kg car moves at 15.0 m/s. What is the magnitude of the horizontal net force needed to bring the car to a halt in a distance of 50.0 m?
Thursday, February 19, 2015 at 8:33pm

Calculus Physics
A particle is subject to a time-dependent force: F(t)=5t√. If the particle's mass is 7 kg, what will its velocity be at t=6.7 seconds, assuming its initial velocity at t=0 is equal to 0.
Thursday, February 19, 2015 at 6:58pm

Algebra
How do you know which rule to use when it doesn't specify? All it says is find the derivative of the function. I haven't had algebra/calculus in over 20 years, I'm completely lost. Please help
Thursday, February 19, 2015 at 5:56pm

business math
How do you know which rule to use when it doesn't specify? All it says is find the derivative of the function. I haven't had algebra/calculus in over 20 years, I'm completely lost. Please help.
Thursday, February 19, 2015 at 5:41pm

Calculus
On planet Calculi, acceleration due to gravity is -20 ft/sec^2. A ball is thrown upward with an initial velocity of 40ft/sec from an initial height of 50. a) Write the equation for the height of the ball, s(t), at time t. b) Find the velocity when the ball hits the ground. c) ...
Thursday, February 19, 2015 at 12:09pm

calculus
When an oil well burns, sediment is carried up into the air by the flames and is eventually deposited on the ground. Less sediment is deposited further away from the well. Experimental evidence indicates that the density (in tons per square mile) at a distance r in any ...
Thursday, February 19, 2015 at 11:00am

Calculus
A spherical balloon with radius 3 inches is partially filled with water. If the water in the balloon is 4 inches deep at the deepest point, how much water is released when the balloon hits the wall and breaks?
Wednesday, February 18, 2015 at 1:39pm

Calculus Physics
A particles with mass 3.7 kg moves in the x direction according to the following function: x(t)=−7+4t+3t2−4t3. (the units of each coefficient are meters, and time is measured in seconds). At time t=7.8, what is the net force acting on the particle?
Wednesday, February 18, 2015 at 10:45am

Calculus Physics
A box and one force vector, F1 is shown. F1 = + 10 N. If the mass of the box is 3 kg, what is the magnitude and direction of a force, F2, that would need to be applied if the box was to have an acceleration of + 2 m/s 2 in the horizontal direction. (Indicate direction by ...
Wednesday, February 18, 2015 at 9:23am

Calculus
Find the volume of the solid obtained by rotating the region bounded by y=8x+24, y=0 about the y-axis.
Wednesday, February 18, 2015 at 1:04am

Pre-calculus
Find the first two terms of a geometric sequence if t_3+ t_4 = 50 and t_4 + t_5 =100? t3= a(r^2) t4= a(r^3) t5= a(r^4) a(r^2)+ a(r^4)= 100 ------------------------- a(r^3)+ a(r^4) = 50 ar^3 ----- = 2 ar^2 r = 2 <-------
Tuesday, February 17, 2015 at 9:03pm

Pre-Calculus
Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ----------------------------------------​ A.This is a divergent series because the absolute value of r is greater than 1. ----------------------------------------​ Q. The first term of an ...
Tuesday, February 17, 2015 at 8:19pm

Calculus
A craftsman wants to make a cylindrical jewelry box that has volume, V, equal to 60 cubic inches. He will make the base and side of the box out of a metal that costs 50 cents per square inch. The lid of the box will be made from a metal with a more ornate finish which costs ...
Tuesday, February 17, 2015 at 7:18pm

calculus A
A particle moves according to a law of motion s = f(t) = t3 - 12t2 + 21t, t 0, where t is measured in seconds and s in feet. v(t) = 3t^2 - 24t 21 a(t) = 6t - 24 e) Find the total distance traveled during the first 8 s. i) When is the particle speeding up? (Enter your answers ...
Tuesday, February 17, 2015 at 6:52pm

Calculus
If f(x) = x4 + 6x,find f'(x).
Tuesday, February 17, 2015 at 5:45pm

Calculus Chain rule
How can derive this function?f(x) = 2/(9x^5+1)^5 The answer is The answer is -450x^4/(9x^5+1)^6 Can you please show why? Thank you
Tuesday, February 17, 2015 at 4:24pm

Calculus: Optimization
I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the ...
Tuesday, February 17, 2015 at 1:55pm

calculus 3
A golf ball is driven down a horizontal fairway with an initial speed of 55m/s at an initial angle of 25 degrees. (Assume the tee from which the ball is hit is of negligible height). a). how far does the ball travel horizontally b). when does the ball land? c). what is the max...
Tuesday, February 17, 2015 at 12:05pm

calculus
An artificially created lake is bordered on one side by a straight dam. The shape of the lake surface is that of a region in the xy-plane bounded by the graphs of 2y=16-x^2 and x+2y=4. Find the area of the surface of the lake.
Tuesday, February 17, 2015 at 11:17am

Calculus
Calculate the area of the bounded region between the curves y^2=x and 3y = -3y + 9 ?
Tuesday, February 17, 2015 at 11:05am

Calculus
Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π]
Tuesday, February 17, 2015 at 12:07am

calculus
s= [b]*[d]+64t-16t^2 what is the greatest height above the ground the rock will go
Monday, February 16, 2015 at 11:26pm

calculus
hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!! A population is modeled by a function P that satisfies...
Monday, February 16, 2015 at 7:04pm

Pre calculus
A tugboat is traveling at 30 miles per hour at a compass heading of 38 degrees. The current is from the direction of 125 degrees moving at 7 mph. Find the resultant speed and the direction of the boat. I understand the concept and that I must use the law of cosines. I got 30^2...
Monday, February 16, 2015 at 4:29pm

Pre-calculus
Let z and w be complex numbers such that |2z-2|=25, |z+2w|=5, and |z+w|=2. Find |z|. I first squared both equations and expressed the square of the magnitudes in terms of the complex numbers and its conjugates. Next, I summed the equations together and attempted to solve for |...
Monday, February 16, 2015 at 4:17pm

Pre-Calculus
he amount M (in billion of dollars) of mortgage debt outstanding in the US from 1990 to 2001 can be approximated by the function M(t)= 29.9t^2 + 3892 where t=0 represents 1990. Rewrite the function so that t=0 represents 2000.
Monday, February 16, 2015 at 10:53am

Calculus
Integrate Cos^7(2x) Explanation would be helpful
Monday, February 16, 2015 at 1:53am

Calculus
determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0<=x<=2pi. This is what i did: 1.) i found the derivative of the function which is f'(x)=cosx+sinx 2.) I set f'(x)=0 and got sinx/cosx=-1 which is tanx=-1 and then x=3π/4...
Sunday, February 15, 2015 at 7:43pm

multivariable calculus
show that a=!0 , the equation p=2asin0cos0 describes the sphere centered(a,0,0) at radius|a|
Sunday, February 15, 2015 at 4:16pm

Pre-Calculus
If r = 1, will a sequence be convergent or divergent?
Sunday, February 15, 2015 at 3:46pm

calculus
Find limit of 2x+1-cosx/3x as x approaches 0?
Sunday, February 15, 2015 at 7:12am

Calculus
Can someone please explain how to solve this type of question? Determine the maximum and minimum value of the function f(x)=3x3^x - 1
Saturday, February 14, 2015 at 10:00pm

Calculus
would the derivative of f(x)=(7^x)(x^7) be f'(x)=(7^x ln7) (7x^6)?
Saturday, February 14, 2015 at 7:00pm

Calculus
a certain radioactive substance is decaying so that at time t, measured in years, the amount of the substance, in grams, is given by the function f(t)=3e^-3t. What is the rate of decay of the substance after half a year: I first found the derivative of f(t)=3e^-3t which is f&#...
Saturday, February 14, 2015 at 6:07pm

Calculus
How would I answer this question? Differentiate the function f(x)=sqrt(cosxsinx)
Friday, February 13, 2015 at 11:19pm

Calculus
1. is the derivative of the function f(x)=5e^(4x-9z) f'(x)= -25e^(4x-9z)? 2. Is the derivative of the function f(x)=e^(2x)-e^(-2x) f'(x)=2e^(2x)+2e^(-2x)? 3. If f(x)=e^-x^-1, would f'(2)=-1/4e^(1/4)?
Friday, February 13, 2015 at 9:05pm

Calculus help and please check answer for a)
The decay of a certain substance is modeled by the function N(t)=100(3+e^(-t/3), where the number of particles is represented by N in a time of t hours. a) what is the initial number of particles? - I set t as 0 and got an answer of 400 particles initially b) determine the ...
Friday, February 13, 2015 at 8:53pm

math calculus
what is the difference between the function 2^x and (1/2)^x?
Friday, February 13, 2015 at 8:49pm

Calculus
A wealthy patron of a small private college wishes to endow a chair in mathematics with a gift of G thousand dollars. Suppose the mathematician who occupies the chair is to receive $110 thousand dollars per year in salary and benefits. If money costs 8% per year compounded ...
Friday, February 13, 2015 at 7:33pm

calculus- min value of function
The answer is -1/2 but how? Which of the following is the minimum value of the function f(x)= sinxcosx? a) 0 b) -1/2 c) -1 d) does not exist
Friday, February 13, 2015 at 7:23pm

Calculus
I am not too sure if I did this question correct. Thanks in advanced! Data table: Time after Consumption (min): 30 60 90 120 150 180 Amount of Codeine in Blood (mg): 27.0 23.5 21.2 18.7 16.6 14.5 1.) create a scatter plot of the data and determine a suitable equation to model ...
Friday, February 13, 2015 at 2:01pm

pre- calculus
In how many ways can a family of six be seated at a round table if the mother and father must sit together?
Friday, February 13, 2015 at 12:28pm

Calculus
Let f(x)=cosxsqrt(1+sinx). A. Let F(x)=the integral of f(x)dx and F(0)=5/3, find F(pi/2). I got 3.386 with U-substitution B. If G(x)=the integral of f(x)sinxdx and G(0)=1/3, find G(x). I got a reply to this but I did not understand the explanation. How would I solve this with ...
Friday, February 13, 2015 at 9:52am

Pre-Calculus
Each second after shut-off, the speed of the blade is 2/3 of the speed in the previous second. After the first 8 s, the saw has turned 258 times. What was the speed of the saw before the motor shut off, to the nearest tenth of a turn per second? I get 805.4 but I don't ...
Friday, February 13, 2015 at 9:07am

calculus
Two forces of 7 lb. and 14 lb. act on a body at right angles to each other. Find the angle their resultant force makes with the force of 14 lb.
Friday, February 13, 2015 at 8:54am

Calculus
The integral of sin(7x)cos(7x)dx
Friday, February 13, 2015 at 4:13am

Calculus
Integration with substitution The integral of f'(g(5x))g'(5x)dx
Friday, February 13, 2015 at 3:37am

Calculus
Let f(x)=cosxsqrt(1+sinx) A. If F(x)=the integral of f(x)dx and F(0)=5/3, find F(pi/2). B. If G(x)=the integral of f(x)sinx dx and G(0)=1/3, find G(x).
Friday, February 13, 2015 at 2:01am

Calculus
f'(x) if x is less than or greater than 1 Let F'(x)={ g'(x) if x>1 Where f'(x)=x/(x^2-2)^2 and g'(x)=3x-4 A. If f(1)=3/2, find f(x) B. If F(x) is continuous at x=1, find g(x). C. Express F(x). D. If F(x) is continuous at x=1, determine if F(x) is ...
Friday, February 13, 2015 at 12:20am

Calculus
Integration with trig functions Integral of [(1-sinx)/cos^2x] dx
Thursday, February 12, 2015 at 11:58pm

Calculus
I am not too sure if I did this question correct. Thanks in advanced! Data table: Time after Consumption (min): 30 60 90 120 150 180 Amount of Codeine in Blood (mg): 27.0 23.5 21.2 18.7 16.6 14.5 1.) create a scatter plot of the data and determine a suitable equation to model ...
Thursday, February 12, 2015 at 11:54pm

Calculus
Integration with U-Substitution Integral of [x/sqrt(x+1)] dx I'm getting confused with how to deal with the x when I find the derivative of (x+1) because they don't match.
Thursday, February 12, 2015 at 11:22pm

Calculus
Suppose f"(x)=6x-2 A. If f'(1)=5, find f'(x). I got f'(x)=3x^2-2x+4 B. Fine the average rate of change of f on [-1,4]. C. Fine the value of x guaranteed by the mean value theorem for r on [-1,4]. D. If f(-1)=-2, find f(x) I am not sure how to do B, C, and D.
Thursday, February 12, 2015 at 10:14pm

Calculus
Integrate: Indefinite integral of [(sqrt(x))-1]^2 / [sqrt(x)] dx
Thursday, February 12, 2015 at 9:54pm

Pre-calculus
Hello, Consider a geometric sequence with t3= 18 and t7= 1458. Are there one or two values for the common ratio? How does this affect the sequence (I got one, but the way this question mentions 2 ratios, I get the feeling there are 2 values.) My work: 1458 = 18r^4 81 = r^4 3 = r
Thursday, February 12, 2015 at 9:29pm

calculus
integral sqrt(1-x^2) . sin^-1 x dx
Thursday, February 12, 2015 at 11:25am

calculus
integral sec^-1 x dx
Thursday, February 12, 2015 at 11:15am

Calculus
What would an example of a logarithmic function that contains a radical within it and a quotient within it where you would need to use chain rule and quotient rule to take derivative look like? How would taking the derivative of the function in its original form look different...
Thursday, February 12, 2015 at 12:14am

Calculus
What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look different when using log ...
Thursday, February 12, 2015 at 12:13am

calculus
A small airplane has an air speed of The pilot wishes to fly to a destination that is 480 km due west from the plane’s present location. There is a wind from the south.
Tuesday, February 10, 2015 at 4:50pm

Pre-Calculus
On a campus of 9000 students, a single student returned to campus with a case of measles on Monday January 5th. The infirmary is keeping track of the number of students who have been diagnosed with the disease Day # of students infected 1. 2 2. 5 3. 9 4. 28 5. 64 6. 81 7. 320...
Tuesday, February 10, 2015 at 12:24am

Pre-Calculus
The Gateway Arch in St. Louis, Missouri is not a parabola but a shape known as a catenary. The name is given to the shaoe formed by the Graph of the hyperbolic cosine (cosh). The arch has a height of 625 feet andna span of 600 feet. The hyperbolic cosine is defined as: Cosh x...
Tuesday, February 10, 2015 at 12:11am

Pre-Calculus
A corpse was discovered in a motel room at midnight and uts temperature was 82°F. The temperature dropped to 80.5°F two hours later. Given k is a constant for the object in question, S is the surrounding temperature, t represents the time and theta(of time) is the ...
Monday, February 9, 2015 at 11:55pm

Calculus
Write the definite integral for the area of the region lying in the upper half of the ellipse given by 4x^2+y^2=4
Monday, February 9, 2015 at 11:43pm

Calculus
The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it will take for the population to reach 50,000.
Monday, February 9, 2015 at 11:38pm

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