Exercise
$\sqrt{x^{2}+y^{2}}=e\arctag^{\frac{7}{2}}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the equation (x^2+y^2)^(1/2)=earctan(x)^(7/2). Removing the variable's exponent raising both sides of the equation to the power of 2. The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(\sqrt{\arctan\left(x\right)^{7}}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{7}{2} and n equals 2. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x^2 from both sides of the equation.
Solve the equation (x^2+y^2)^(1/2)=earctan(x)^(7/2)
Final answer to the exercise
$y=\sqrt{e^2\arctan\left(x\right)^{7}-x^2},\:y=-\sqrt{e^2\arctan\left(x\right)^{7}-x^2}$