8005

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?

8004

Mathematics Matrices Level: Misc Level

$\begin{bmatrix} x+3 & 2 \\ -3 & x \end{bmatrix}$   = 10

Solve for x

8003

Mathematics Logarithm Level: Misc Level

Find;(a)antilog 92 (b)antilog8 (-2)

8002

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.

8001

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?

8000

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?

7999

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

7998

Mathematics Differential Equations Level: Misc Level

Question in Q7999

7997

Mathematics Calculus Level: Misc Level

Solve the initial value problem dy/dx = y3 ,y(0)=1

7994

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

7993

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.

7992

Chemistry Organic Chemistry Level: Misc Level

Show all the steps and all the reagents needed to transform formaldehyde into 4-propyl-4-heptanol.

7991

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.

7990

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;

7989

Chemistry Organic Chemistry Level: Misc Level

Draw complete structures for;

(a)1,1,1-trichloro-5,5-dimethyl-2-octanone

(b) z-2,3-dichloropropenal

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