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Evaluate the multiple integral under given condition using spherical coordinate.
Let T be the three dimensional region that lies outside the sphere x2 + y2 + z2 = 1 but inside the sphere x2 + y2 + z2 = 4. Convert the following triple integral to an appropriate coordinate system and evaluate: ∫∫∫(Z2 / x2 + y2 + z2) dv
The second number is 2 more than the first. What are the possible values for the first of the two numbers?
Find all lines through the point (2,1) that are tangent to parabola y=xsquared. What properties of parabolas and formulas do you use to solve this problem?
Evaluate the number of license plate from the given data - how many different groups of 4 are made up of 2 boys and 2 girls?
What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?
Ally earns $2500 per month plus commission of 7%. Her total monthly earnings (P) is represented by P=2500+.07t where (t) equals total sales for the month. What is the equation that represents total monthly earnings (P) if her commission increases ..
A book case is 1.98 meters tall and its shelves aree 33 cm apart. how many shelves are in the bookcase?
One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations of X and Y.
Let R(t) be the field of rational functions. Answer the following (with proofs): If we identify the rational numbers with a subset of R(t), what function corresponds to a given rational number r?
A popular flashlight that uses two D-size batteries was selected, and several of the same models were purchased to test the "continuous-use life" of D batteries. As fresh batteries were installed, each flashlight was turned on and the time noted.
Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
Correlation between competence Scores and Internal Scores
Find the parametric equations for the line through the point P = (3, -4, 0) that is perpendicular to the plane 2x + 0y+ 5z = 1. Use "t" as your variable, t = 0 should correspond to P
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