Triangle & Rectangle Area Calculator: Find Solutions for x and y with exponents

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In summary, the Triangle & Rectangle Area Calculator is a tool that allows users to find solutions for the areas of triangles and rectangles using exponents for x and y. This calculator is useful for quickly calculating the areas of these shapes without having to manually calculate them. By inputting the necessary values, users can easily obtain the area of a triangle or rectangle with exponents for x and y. This calculator is a helpful tool for students, mathematicians, and anyone in need of quick and accurate area calculations for these shapes.
  • #1
mathelord
i need help with area of rectangle with sides x^x^x^x^x^x...
and y^y^y^y^y... where x is 800^(1/800)
and y is 600^(1/600). leaving answer in whole number not exponent
 
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  • #2
If x^x^x... (an infinite "tower") is equal to A, then x^(A)= A so x= A^(1/A).
Here x= 600^(1/600) so x equals what? You can find y in exactly the same way and then find the area of a rectangle.

Why was this titled "help with triangle"?
 
  • #3


First, let's clarify that the expression x^x^x^x^x^x is not a valid mathematical expression. It is important to use parentheses to indicate the order of operations. Assuming you meant (x^x)^x, the area of the rectangle would be x^(2x). Similarly, the area of the triangle would be (x^(2x))/2.

Now, let's plug in the given values for x and y. We can simplify x^(2x) by using the properties of exponents. Since x is equal to 800^(1/800), we can rewrite x^(2x) as (800^(1/800))^(2(800^(1/800))). Using the power rule of exponents, we can simplify this to 800^(2(1/800)). This can be further simplified to 800^(2/800) or 800^(1/400).

Similarly, we can simplify y^(2y) to 600^(1/300).

Therefore, the area of the rectangle would be 800^(1/400) and the area of the triangle would be (800^(1/400))/2. Since the instructions specify leaving the answer in whole number, we can round the decimal approximation of 800^(1/400) to the nearest whole number. Similarly, we can round (800^(1/400))/2 to the nearest whole number.

In summary, the area of the rectangle with sides x^x^x^x^x^x and y^y^y^y^y would be approximately 1, and the area of the triangle would be approximately 0.
 

1. How does the Triangle & Rectangle Area Calculator work?

The calculator uses the formula for finding the area of a triangle and rectangle, which is base x height. It then solves for x and y by using the given exponents and solving the resulting equations.

2. Can I use this calculator for any type of triangle or rectangle?

Yes, the calculator can be used for any type of triangle or rectangle as long as the given measurements are in the correct units (e.g. centimeters, inches, etc.)

3. What if I have more than one unknown variable in my equation?

The calculator can only solve for one unknown variable at a time. If you have more than one unknown, you will need to rearrange the equation and use the calculator multiple times to solve for each variable.

4. How accurate are the solutions provided by the calculator?

The solutions provided by the calculator are accurate to the given number of decimal places. However, rounding errors may occur if the given measurements are not precise.

5. Is there a limit to the number of exponents that can be used in the calculator?

No, there is no limit to the number of exponents that can be used. The calculator can handle any number of exponents as long as they are in a valid mathematical format.

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