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May 2010

Calculate the acute angle between 2x - 4y - z = -5 and 3x + 4y + 5z = -6

Problem
Calculate the acute angle between two intersecting surfaces whose equations are as follows:
$$2x - 4y - z = -5$$

$$3x + 4y + 5z = -6$$

A.   62.4° C.   42.6°
B.   64.2° D.   46.2°

 

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If arcsin (3x - 4y) = 1.571 and arccos (x - y) = 1.047, what is the value of x?

Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?

A.   0.5 C.   1.5
B.   1.0 D.   2.0

 

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A solid spherical ball remolded into a hollow spherical ball

Problem
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.

A.   1.3 cm C.   1.2 cm
B.   1.5 cm D.   1.6 cm

 

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