on the graph below are three points X. Y, and z. write the coordinates for the...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
1. Using polar coordinates in the x-y plane, find the volume of the solid above the cone z r and below the hemisphere z= v8-r2. As a check the answer is approximately 13.88 but of course you have to calculate the exact answer 2. At the right is the graph of the 8-leafed rose r 1+2cos(40) Calculate the area of the small leaf. As a check the answer is 0.136 to 3 places of decimal (But of course you have...
three a) Sketch the graph and complete the table for the polar equation 5-2cose Type of conic section (x, y) coordinates of vertex or vertices Eccentricity (x,y) coordinates of the focus or the foci (x,y) coordinates of the x intercept (x,y) coordinates of the y intercept Domain in interval notation Range in interval notation (x,y) equation of the directrix or directrices (x,y) coordinates of the center Standard equation in (x,y) variables
three a) Sketch the graph and complete the table...
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately- three decimal places) the area of the region bounded by the curves. Also, make a rough sketch of the region sought. You must write the definite integral using proper notation to receive full credit 1) y = χ sin(x*) , y = x6
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves....
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
Consider the function f and region E. f(x, y, z) = y, E = {(x, y, z)| 1 5 x2 +3? 59,0 SyS 1 - x2 - 22; (a) Express the region E in cylindrical coordinates. O E = {(r, 0, 2)Iisrs9,0 SO S 21,0 S 231-23 O E = {(1, 0, 2)| 1 575 3,0 SOST,O SZS 1-12} O E = {(r, 0, 2)Ii Srs 3,0 s E s 2,0 S 25 1 - 2 O E = {(r,...
Need answer all question and draw
Below is the graph of y= f'(x). Use the graph to answer the questions that follow. -4 -3 1. On what intervals is f(x) decreasing? Write your answer in interval notation. 2. What is the total change in f as x goes from 1 to 2? 3. At what value(s) of x does take on a local maximum? If there are none, write "NONE" in the answer space. 4. If f(-2)=-3, what is the...
3. (10 points) A solid of revolution V has a volume of 4 cubic units and cross-sectional slices of area A(2), where x ranges frorn 0 to 1 . The graph of A(z) İs given below, along with the graphs of three other functions. Which one is the graph of A()? Justify your answer (a) y (c) yt (d) y 0 -6 0
3. (10 points) A solid of revolution V has a volume of 4 cubic units and cross-sectional...
Consider the function below. y z= 2+x+ (a) Match the function with its graph (labeled A-F). (b) Match the function with its contour map (labeled 1-VI). O V VI Give reasons for your choices. Select- Also, the values of z approach 0 as we use This function is not periodic, ruling out the graphs in (b) Match the function with its contour map (labeled I-VI) II III IV V VI Give reasons for your choices. This function is not periodic,...
Consider these three moment generating functions, for X, Y and Z: (5 points each) m (t)=W-3 m, (t)=e + m,(t)=eW-7 a. What is the mean of X? b. What is the mean of Y? c. What is the mean of Z? d. What is the variance of X? e. What is the variance of Y? f. What is the variance of Z? Consider independent random variables X and Y with the following pmfs: y=1 (0.5 x=1 S(x)= {0.5 x =...