Just a simple calculus question

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In summary, calculus is a branch of mathematics that deals with continuous change and involves the analysis of functions, rates of change, and accumulation of quantities. It is important because it provides a framework for understanding and solving complex problems in various fields. The two main branches of calculus are differential and integral calculus, which respectively deal with rates of change and accumulation of quantities. Calculus is widely used in real-life applications, such as determining maximum and minimum values, calculating velocity and acceleration, and predicting growth and decay. While it can be challenging to learn, with proper study and practice, anyone can understand its fundamental concepts and applications.
  • #1
Lisa...
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Why does
((v0^2 sin (2a))/2g) + ((v0 cos a)/g) sqrt(v0^2 ((sin^2)a) +hg) equal
((v0^2 sin (2a))/2g) (1+ sqrt(1+((2hg)/(vo^2) (sin^2)a))) ?
 
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  • #2
Multiply the right-hand term on the lhs by sin(a) and divide the sq root term by sin²(a) to balance out.
Take out the Vo term from inside the sq root and you should have Vo².sin(2a)/2g as a commom factor.

Let me guess: this to find the angle of elevation for maximum range when firing off a cliff of height h, yes ?
 
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  • #3
Exactly! Wow thanks a hell of a lot!
 

1. What is calculus?

Calculus is a branch of mathematics that deals with the study of continuous change. It involves the analysis of functions, rates of change, and the accumulation of quantities.

2. Why is calculus important?

Calculus is important because it provides a framework for understanding and analyzing complex phenomena in various fields, such as physics, engineering, economics, and statistics. It also helps in solving practical problems and making predictions.

3. What are the two main branches of calculus?

The two main branches of calculus are differential calculus and integral calculus. Differential calculus deals with the study of rates of change and slopes of curves, while integral calculus deals with the accumulation of quantities and the calculation of areas under curves.

4. How is calculus used in real life?

Calculus is used in various real-life applications, such as determining the maximum or minimum value of a function, finding the velocity and acceleration of moving objects, calculating the area and volume of irregular shapes, and predicting the growth and decay of populations.

5. Is calculus difficult to learn?

Calculus can be challenging to learn, as it requires a solid understanding of algebra and trigonometry. However, with proper study and practice, anyone can understand the fundamental concepts and applications of calculus.

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