answer:1. **Determine the surface area of the original can**: Given that the surface area of the original can is (300 , text{cm}^2), we start with the formula for the surface area of a cylinder: [ 2 pi r^2 + 2 pi r h = 300. ] 2. **Calculate the surface area when the radius is doubled**: If the radius is doubled, the new radius is (2r). Plugging this into the surface area formula: [ 2 pi (2r)^2 + 2 pi (2r) h = 2 pi cdot 4r^2 + 4 pi r h. ] Simplifying this expression: [ 8 pi r^2 + 4 pi r h = 900. ] 3. **Compare the equations**: From the original surface area equation, multiply by 3: [ 3 cdot (2 pi r^2 + 2 pi r h) = 3 cdot 300. ] Which gives: [ 6 pi r^2 + 6 pi r h = 900. ] Compare this with the surface area when the radius is doubled: [ 8 pi r^2 + 4 pi r h = 900. ] 4. **Isolate terms**: Subtract the second equation from the first to isolate the terms involving (r) and (h): [ (6 pi r^2 + 6 pi r h) - (8 pi r^2 + 4 pi r h) = 0. ] Simplifying, we get: [ -2 pi r^2 + 2 pi r h = 0. ] Divide by (2 pi): [ -r^2 + r h = 0. ] This implies: [ r h = r^2 quad text{or} quad h = r. ] 5. **Express initial conditions**: Substitute (h = r) into the original surface area equation: [ 2 pi r^2 + 2 pi r r = 300. ] Simplifying, we have: [ 4 pi r^2 = 300, ] [ pi r^2 = 75. ] 6. **Calculate the surface area when the height is doubled**: When the height is doubled, height becomes (2h) (which is (2r)). Substituting into the original formula: [ A = 2 pi r^2 + 2 pi r (2r). ] Simplifying, [ A = 2 pi r^2 + 4 pi r^2, ] [ A = 6 pi r^2. ] Using the relation (pi r^2 = 75): [ A = 6 cdot 75, ] [ A = 450 , text{cm}^2. ] # Conclusion: The surface area of the can when the height is doubled is ( boxed{450 , text{cm}^2} ).

answer:Objective-C is a general-purpose, object-oriented programming language that was developed by Brad Cox and Tom Love in the 1980s. It is a superset of the C programming language, adding features for object-oriented programming and runtime binding. Objective-C was the primary programming language used for developing software on Apple's platforms, including: 1. macOS (formerly Mac OS X) 2. iOS (for iPhone and iPad) 3. watchOS (for Apple Watch) 4. tvOS (for Apple TV) It was used to build a wide range of applications, from desktop software to mobile apps. Many popular iOS and macOS apps, such as Safari, Mail, and iTunes, were built using Objective-C. However, in 2014, Apple introduced Swift, a new programming language designed to replace Objective-C as the primary language for Apple's platforms. Since then, Swift has become the preferred language for new projects, and many existing Objective-C projects have been migrated to Swift. Despite this shift, Objective-C is still maintained and supported by Apple, and many legacy projects continue to use it. Additionally, Objective-C is still used in some third-party frameworks and libraries, and it remains a viable option for developing software on Apple's platforms. In summary, Objective-C is a powerful, object-oriented programming language that was widely used for developing software on Apple's platforms, but it has largely been replaced by Swift as the primary language of choice.

answer:The best current alternative to Objective-C for developing software on Apple's platforms is Swift. Apple introduced Swift in 2014 as a replacement for Objective-C, and it has since become the preferred language for building iOS, macOS, watchOS, and tvOS apps. Swift offers several advantages over Objective-C, including: 1. **Easier to learn**: Swift has a more modern and intuitive syntax, making it easier for new developers to learn and for existing developers to transition from other languages. 2. **Improved safety**: Swift has built-in safety features, such as optional types and memory management, which help prevent common errors and make code more reliable. 3. **Better performance**: Swift is designed to be fast and efficient, with performance that rivals Objective-C. 4. **Growing ecosystem**: Swift has a rapidly growing ecosystem of libraries, frameworks, and tools, making it easy to find resources and support for your projects. 5. **Full Apple support**: Swift is fully supported by Apple, with extensive documentation, tutorials, and development tools available. Some other alternatives to Objective-C, such as React Native and Flutter, allow you to build cross-platform apps using languages like JavaScript and Dart. However, if you're specifically targeting Apple's platforms and want a native, high-performance experience, Swift is the best choice. Here's a rough estimate of the trade-offs between these alternatives: * Swift: Best for native Apple experiences, high performance, and ease of use ( Learning curve: 2-6 months) * React Native: Good for cross-platform development, JavaScript familiarity, and fast development (Learning curve: 1-3 months) * Flutter: Good for cross-platform development, fast development, and a growing ecosystem (Learning curve: 1-3 months) Keep in mind that the learning curve and trade-offs can vary depending on your specific needs, experience, and goals.

answer:While loops, for loops, and do-while loops are all used for repetitive execution of a block of code, but they differ in their syntax and usage: **While Loop** A while loop repeats a block of code as long as a specified condition is true. The condition is checked before the code is executed, so if the condition is initially false, the code is not executed at all. Example: ```c int i = 0; while (i < 5) { printf(%d , i); i++; } ``` **For Loop** A for loop repeats a block of code for a specified number of iterations. It consists of three parts: 1. Initialization: `i = 0` 2. Condition: `i < 5` 3. Increment/Decrement: `i++` Example: ```c for (int i = 0; i < 5; i++) { printf(%d , i); } ``` **Do-While Loop** A do-while loop repeats a block of code as long as a specified condition is true, but it guarantees that the code is executed at least once. The condition is checked after the code is executed, so even if the condition is initially false, the code is still executed once. Example: ```c int i = 0; do { printf(%d , i); i++; } while (i < 5); ``` Key differences: * **Initialization**: For loops have a built-in initialization step, while while loops and do-while loops require manual initialization. * **Condition checking**: While loops check the condition before executing the code, while do-while loops check the condition after executing the code. For loops check the condition before each iteration. * **Guaranteed execution**: Do-while loops guarantee that the code is executed at least once, while while loops and for loops do not. Choose the loop that best fits your use case: * Use a while loop when the condition is complex or needs to be checked before executing the code. * Use a for loop when you know the number of iterations in advance or need to iterate over a range of values. * Use a do-while loop when you need to guarantee that the code is executed at least once, even if the condition is initially false.