Mathematics Complex Numbers Level: Misc Level
Multiply (7 cis 68o) (-2 cis 82o) and express the answer in rectangular coordinates. Give an exact answer.
Mathematics Arithmetic Level: Misc Level
If n varies inversely as m2, directly as p, and directly as the square root of t. What happens to n when t is multiplied by 9,p is doubled, and m is multiplied by 6?
Mathematics Matrices Level: Misc Level
= 10
Solve for x
Mathematics Logarithm Level: Misc Level
Find;(a)antilog 92 (b)antilog8 (-2)
Mathematics Conics Level: Misc Level
A parabola has its vertex at(-3,2) and its focus at (-3,-2).Write the equations of the parabola, the directrix, and the axis of symmetry.Graph the parabola.
Mathematics Conics Level: Misc Level
The reflecting surface of a parabolic antenna has the shape formed when the parabola y=(1/28)x2 is rotated about its axis of symmetry. If the measurements are in feet, how far from the vertex should the receiver be placed if it is to be at the focus?
Mathematics Calculus Level: Misc Level
Suppose that a motorboat is moving at 30 ft/sec when its motor suddenly quits,and that 5 seconds later the boat has slowed to 15 ft/sec.Assume that the resistance it encounters while coasting is proportional to its velocity.How far will the boat coast in all?
Mathematics Differential Equations Level: Misc Level
Find the particular solution of the differential equation dy/dx + 3y = 5x
subject to the initial condition y(1)=1.
* Answer continued in Q number 7998
Mathematics Differential Equations Level: Misc Level
Question in Q7999
Mathematics Calculus Level: Misc Level
Solve the initial value problem dy/dx = y3 ,y(0)=1
Mathematics Differential Equations Level: Misc Level
First find a general solution of the differential equation dy/dx = 3/y
Then find a particular solution that satisfies the initial condition y(o)=5
Chemistry Organic Chemistry Level: Misc Level
There is only one oxime formed from 3-pentanone.However, 2-pentanone forms two diastereomeric oximes. Draw their structures.
Chemistry Organic Chemistry Level: Misc Level
Show all the steps and all the reagents needed to transform formaldehyde into 4-propyl-4-heptanol.
Chemistry Organic Chemistry Level: Misc Level
With acid-catalysis, one mole of cis-1,2-cyclopentadiol readily forms an acetal with formaldehyde whereas one mole of trans-1,2-cyclopentadiol does not.Explain with the aid of structural formulas.
Chemistry Organic Chemistry Level: Misc Level
Grignard reagents are not the only carbon nucleophiles.Recall the SN2 reactivty of the conjugate base of a terminal alkyne(see Exercise 4 in Lesson 8).Draw structures for the products in the following sequence;
