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Let R be the region in the first quadrant bounded by the curves y = 9x and y = x3.
a. Sketch the region R and calculate its area.
b. Calculate the volume of the solid of revolution obtained by rotating the region R around the vertical line x = 5 , and draw a typical layer which appears in the calculation of volume (disc, washer or cylindrical shell), labeling its dimensions.
3.Suppose thet g . odd, f°,g(x)d.3 = 2, wed g(3). = Either find f: g(g)dx, or show there is not enough informotion to .a g(3.1.3.Suppose that g is odd, R 4−2g(x) dx = 2, and R −4−6g(x) dx = 3. Either find R 62g(x) dx, or show there is notenough infor..
Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five. Set up a system of linear equations to represent the two angles.
A conical water tank with vertex down has a radius of 10 feet at the top and is 29 feet high. If water flows into the tank at a rate of 20 {rm ft}^3{rm /min}, how fast is the depth of the water increasing when the water is 13 feet deep?
"Show that the indicated function is a solution of the given differential equation; that is, substitute the indicated function for y to see that it produces an equality"
Evaluate the expression for the given value of x
Telephone rate. A second long-distance telephone service charges $0.09 per minute or fraction thereof for calls lasting 10 minutes or more and $0.18 per minute or fraction thereof for calls lasting less than 10 minutes.
Determine the probability on sales
Consider the constants A, B, C and the function f(x, y) = Ax^2 + Bxy + Cy^2. Show that the only choice of coefficients A, B, C giving ∂^2f/∂x^2+∂^2f/∂y^2= 2,
Conditional Probability of Drawing Different Kinds of Cards. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting
What is the greatest number of poster boards Adam can make if he uses all of the stamps?
What are the most signification concepts that you have learned about the physical and social domains on the basis of your reading and experience with children?
The region R is the base of a solid. For this solid, at each x the cross section perpendicular to the x-axis is semicircle. Find the volume of this solid using a representative shape.
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