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

[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

 

[HallsofIvy]

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"?

 

[thepatientmental]

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.