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- Eliminate the parameter t x = 4sin t-4, y = 4cos t-3 GRAPH using a table of values or sketchA large tank is formed by rotating the graph y=x3 (0, 2) about the y-axis. The tank is 8 feet tall and has a diameter of 4 feet at its top. If the tank is full of maple syrup with density 85 ??/??3 , find the exact work required to pump the syrup out of the top of the tank.Calculate ∫ ∫arctany/xdA, where R={(x, y) / x2 + y2 < 4, x2 + y2 21, y = x < 0}. (show with graph)
- The graph of y=f(x) is shown in blue. Draw the graph of y=2f(x), shown in red, by determining how a stretch or compression will transform the location of the indicated blue points. Drag the movable red points to the desired coordinates.You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. Your design team has coded this in-game world to exist on the circle x^2 + y^2 ≤ 900 on the xy-plane. At any point (x,y) in this world you've also associated a danger function d(x,y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x,y) correspond to safe points. If d(x,y) = e^(-x^2)(y), find the safest point(s) and most dangerous point(s) in-game.Graph of y = sin 1/x . The discontinuity at x = 0 is not a jump, removable, or infinite discontinuity.
- x + y = 3 Find the x and y intecepts to be put on a graphA point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt - Rsin(t), R - Rcos(t). One arch of the cycloid is completed from t=0 to t=2pi. Show that the length of this arch is always four times the diameter of the rolling circle.The equation of a curve is y = x + 2cos x. Find the x co-ordinates of the stationary points of the curve for 0
- x = y3 + 2y: 1. Make a table of values and sketch the graph of the equation. 2. X-ints and y-ints. 3. Test symmetry.Consider the following graph. An S-shaped curve is graphed on the x y coordinate plane. It enters the viewing window at approximately (−3, −1.9), goes up and to the right, passes through the negative y-axis at approximately (0, −1.25), and continues up and right until it reaches the approximate point (0.7, −0.7). It then turns left but continues up, passes through the negative y-axis again at approximately (0, −0.1), passes through the negative x-axis at approximately (−0.2, 0), and continues left and up until it reaches the approximate point (−0.8, 0.8). It then turns to the right but continues up, passes through the positive y-axis at approximately (0, 1.3), and exits the right side of the viewing window at approximately (3, 1.8). Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter NAF in all blanks.) domain=range=FGH has vertices F (-2,1) , G(-2,4) and H (0,2) . Graph FGH . Then reflect it across the X-axis and translate it 3 units down
