Use a double integral to find the area of the region. The region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ). Can someone explain to me where to get the limits of integration for θ? I get how to get the pi/3 and -pi/3 but most examples of this problem show further that you have to do more for the limits of integration but I do not get where they come from?
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Find the work it would take to build a limestone pyramid with a square base with sides 560 ft and a height of 400 feet. (the density of limestone is 150 lb/ft^3)
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Let r(t) = (cos(πt), sin(πt), 3t). Calculate r'(t), T(t) and evaluate T(1).
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Explain, in your own words, what a derivative represents geometrically.
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A boat leaves a dock at 2:00 PM and travels due south at a speed
of 15 km/hr.
Another boat has been heading due east at 20 km/hr and reaches the
same dock at
3:00 PM. How many minutes after 2:00 PM were the two boats closest
together?
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Find all values of x on the interval -4< x< 3 for which the graph of g has a point of inflection. Give a reason for your answer.
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The quantity of a drug,Q, mg, present in the body t hours after an injection of the drug is given is
Q=f(t)=100te1-.5t
find f(1),f'(1),f(10) and f'(10). give units and interpret the answers
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A vat holds 20 cubic feet of liquid and is initially full. Water containing 6 grams of salt per cubic foot is being poured into the vat at the rate of 4 cubic feet per minute, and is instantly mixed. The mixed liquid is draining from the vat at 4 cubic feet per minute, so the vat is always full. Let y(t) denote the number of grams of salt in the vat after t minutes. Write the differential equation for y(t) and use the graphical method to sketch two substantially-different solutions
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A company plans to design an open top rectangular box with square base having volume 4 cubic inches. Find the dimension of the box so that the amount of materiel required for construction is minimal.
(a) Find the dimension of the box so that the amount of materiel required for construction is minimized.
(b) What is the minimized material required for the construction?
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How do you define the area of the region between the graphs of two continuous functions? When calculating the area between two curves, explain, in your own words, the significance of a negative result. Justify your answers with a thorough explanation of the mathematical concepts involved.
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(2)Please determine : FIRST: (A) W’(X) ; THEN: (B) W’(0); W(X)
IS DEFINED BELOW:
W(X) = [ (10* (X^4) ) – 8 ] * { [ (30*X ) + 25 ] ^ (0.5) }
HOWEVER, YOU MUST USE LOGARITHMIC DIFFERENTIATION, NOT THE PRODUCT
RULE; IMPORTANT NOTE : YOU WI LL NOT BE GIVEN A N Y CREDIT FOR USE
OF THE PRODUCT RULE, IN ORDER TO OBTAIN THE DERIVATIVE OF T(X)
!
SERIOUSLY – YOU M U S T USE O N L Y LOGARITHMIC DIFFERENTIATION
HERE !
HINT: (A) FIRST , TAKE “ Ln “ of BOTH SIDES; THEN, DIFFERENTIATE
IMPLICITLY, PARTLY WITH USE OF THE CHAIN RULE; THEN, SOLVE FOR
W’(X). FINALLY, PLEASE
ALSO remember to EVALUATE W’(X) at X =0, to complete YOUR PART (B)
WORK !
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Find the Fourier series of the function.
c. f(t) = sin(3pit), -1</ t </ 1
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Find the total area between y=25-x2 and the x-axis for
0≤x≤7.5.
Round your answer to three decimal places.
The total area between y=25-x2 and the x-axis is what?
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Determine whether the following statements are true or false, and give an explanation or a counterexample.
(a) log3y< log2y for y> 1
(b) The domain of f(x) = ln(x^2) is x > 0
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