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Most applications will need to deal with files stored on disk in one way or another. So far in this book, we really haven t dealt much with this topic (except for a bit of discussion about Core Data and its data stores), so let s remedy that right now. Cocoa actually includes several useful classes for dealing with files in a number of ways. There are classes that provide APIs mimicking operations the user can normally do in the Finder, and others that represent a file in an abstract way. Still other classes have built-in functionality for reading and writing files.

How are the velocities of the ball, before and after the collision, related to the force acting on it Newton s second law of motion describes how the 10 104 velocity of an object is changed by a net force acting on it The change in velocity of the ball must have been caused by the force exerted by the bat on 50 103 the ball The force changes over time, as shown in Figure 9-1 Just after contact is made, the ball is squeezed, and the force increases After the force 00 15 05 00 05 10 15 10 reaches its maximum, which is more than 10,000 times the weight of the ball, the ball recovers its Time (ms) shape and snaps away from the bat The force rapidly returns to zero This whole event takes place within about 30 ms Figure 9-1 The force acting on a baseball increases, then rapidly How can you calculate the change in velocity of the baseball

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decreases during a collision, as shown in this force-time graph Force (N)

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To solve an equation means to find the value of the variable that makes the equation a true statement To solve equations, apply the distributive property and the properties of equality Any properties of equalities that you apply on one side of an equation, you also must apply on the other side Distributive property For any numbers a, b, and c, a(b c) ab ac a(b c) ab ac Example: Use the distributive property to expand the following expression 3(x 2) 3x (3)(2) 3x 6 Addition and subtraction properties of equality If two quantities are equal and the same number is added to (or subtracted from) each, then the resulting quantities also are equal a c b c a c b c Example: Solve x x x 3 3 3 x Example: Solve t t t 2 2 2 t 7 7 10 2 5 5 7 2 5 using the subtraction property 3 3 7 using the addition property

Multiplication and division properties of equality If two equal quantities each are multiplied by (or divided by) the same number, then the resulting quantities also are equal ac bc a b , for c 0 c c 3 using the multiplication property

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UPDATE table SET column = value [WHERE condition]

Several classes in Cocoa, such as NSString, NSData, NSArray, and NSDictionary, provide methods for reading data directly from a file, or writing their contents directly to a file, using just a string containing the full path to the relevant file. For instance, if you want to read the entire contents of a file into a string, you can do something as simple as this:

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Suppose an equation has more than one variable To isolate a variable that is, to solve the equation for a variable write an equivalent equation so that one side contains only that variable with a coefficient of 1 Connecting Math to Physics Isolate the variable P ( pressure) in the ideal gas law equation PV

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NSString *myString = [NSString stringWithContentsOfFile:@"/path/to/something" usedEncoding:NULL error:NULL];

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If a and n are real numbers, n 0, and a 2 n, then a n Connecting Math to Physics Solve for v in Newton s second law for a satellite orbiting Earth

When using the square root property, it is important to consider for what you are solving Because we solved for speed in the above example, it did not make sense to use the negative value of the square root Also, you need to consider if the negative or positive value gives you a realistic solution For example, when using the square root property to solve for time, a negative value may give you a time before the situation even started

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