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Find x if, 2^sin²x + 2^cos²x = 3
Use a membership table to show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
Compute the area of the plane region bounded by the curve x=y2-2 and the line y=-x using integration along the y-axis.
What is the symbolic word if Caroline is late (l), we will not pursue our plan (~p). We did not pursue our plan. Therefore, Caroline was late.
There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 2 or a multiple of 3?
Use the grid to illustrate: 2 5 of 3 4 . Show the strategy clearly by using different types of shading. (4)
Show that the square of an even number is an even number using a direct proof.
531341534531453+145412544531846513468
A bowl has pieces of papers with numbers 2,4, and 6. A piece of paper is chosen at random two times to
form two-digit number. Construct a table for sampling distribution of sample means and identify the 3 specific
properties of the distribution.
Consider the 3-dimensional vector field F defined by F(x,y,z)=(2xyz,x²z+2yz²,x²y+2y²z+e^z).
1.write down the Jacobian matrix jf(x,y,z).
2.determine divF (x,y,z).
3.determine curl F (x,y,z).
4.does F have a potential function? Give reasons for your answer, referring to the relevant definitions and theorems in the study guide.
5.find a potential function of F .
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