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A major-league pitcher releases a ball at a point 6 feet above the ground and 58 feet from home plate at a speed of 100 mi/hr ,  

If gravity had no effect, the ball would travel along a line and cross home plate 4 feet off the ground. Find the drop D caused by gravity.                                                                                                                                                      


NB: in this problem the angle alpha is the angle between the horizontal and the direction of the released ball. Since the ball is dropping, alpha will be negative.

Please help me plot the graphs of the following equations:-

eq1 := diff(E[X(t)], t) = lambda-delta*E[X(t)]-beta*E[X(t)*V(t)];
 eq2 := diff(E[Y(t)], t) = -delta*E[Y(t)]+beta*exp(-rho*tau)*E[X(t)*V(t)];

eq3 := diff(E[V(t)], t) = gamma+N*kappa*E[Y(t)]-mu*E[V(t)]-beta*E[X(t)*V(t)]
NB:- E[X(t)]= the expected value of variable X at time t. 
Please help me know how to input this...


I am working on a problem that I can't seem to figure out the plot commands in Maple. The problem is this...

Given a family of surfaces described by z=(ax^2 +by^2)*(exp(-x^2*-y^2))

I need to obtain a 3D plot of these surfaces and, from the graph of the surfaces, explain how constants a and b will change the shape of the graph. I cannot find the syntax required so plot such a function, but I have been trying using spacecurve(). Does the equation...

I recently noticed that the symbol font in my maplets was not appearing correctly when I ran them using Maple 13 or 14 on my Windows 7 laptop. Additional testing showed that while this was pretty standard on Windows 7, it happened on some, but not all, Windows XP systems.

By a stroke of fortune, my local inquiries about this problem suggested that I look at the Clear Type effect that can produce sharper results, particularly on newer LCD displays.

Before going into too many details, let's look at an example. Here's the code for a simple maplet:


alphabet := "abcdefghijklmnopqrstuvwxyz":

  Window[mainWin](title="Font Test", [
    [ "The two lines of text should show the alphabet in the Times font and then\n the Symbol font, but sometimes the Symbol font is not correctly rendered." ],
    [ "Times ",    Label( alphabet, font=Font("Times",18) ) ],
    [ "Symbol",    Label( alphabet, font=Font("Symbol",18) ) ],
    [ Button( "Done", Shutdown() ) ],
    [ "Version: ", Label( convert(interface(version),string) ) ]
Maplets[Display]( TestFont );

Copy these lines to a Maple worksheet (or document) and execute them, or save them to a text file with file extension .maplet, then double click on the file. The maplet should display two copies of the alphabet, the first with Times Roman font, the second with Symbol font. (The version of Maple running the maplet is given at the very bottom of the maplet.)

If you are running Maple 12 or older, I expect you'll see two different versions of the alphabet, like this:

If you are running Maple 14, I expect the line that should be in Symbol font will be in a poor quality Latin font, like this:

I can't predict which outcome you will see if the maplet is run in Maple 13.

What controls this behavior is the "effects" setting for the appearance settings for your display. If you are using the Clear Type effect, you will not see the Symbol font.

This problem is appearing now because up until Windows 7, the ClearType effect was not the default.

Along with the change in the default effect, the way in which users control the effect changed with the introduction of Windows 7.

Prior to Windows 7, access the Properties popup by right-clicking on your desktop. Then select the Appearance tab and click on the Effects button. In the second dropdown menu you can choose either Standard or ClearType. To see the symbol font (in Maple 13 and later), make sure this is set to Standard.

In Windows 7, go to the start menu and search for cttune.exe. Start the ClearType Text Tuner application. In the first popup window, be sure the Turn on ClearType box is unchecked. (For full instructions, including screenshots, please see .)

When this effect is toggled, the effect changes immediately.

I can't call this a bug, but it is something that I think should be included somewhere in Maple's documentation.

Thanks for listening, I hope this is of use to someone else

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