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Solve for x in a radical equation.
October 30, 2024
The solution to the equation \sqrt{7 + \frac{3}{\sqrt{x}}} = 7 - \frac{9}{x} is x = \frac{9}{4}.
Find the value of x^10 / x^10
October 30, 2024
The solution involves finding an expression for X_n, a sum of reciprocals of powers of x, using the formula for a finite geometric series. Then, the expression for x^n is used to simplify the ratio x^n / X_n, ultimately resulting in x^(n+1).
Find the value of x given two angles that form a right angle.
October 30, 2024
To find x, supplementary angles 5x and 4x are used, along with the fact that the sum of the interior angles of a quadrilateral is 360 degrees. Solving the equation 9x = 180 yields x = 20.
Find the value of R*S
October 29, 2024
The solution demonstrates how to find the value of RS by expanding the second equation, substituting the first equation, and simplifying the resulting equation.
Solve for the unknown variable in an equation.
October 29, 2024
The solution for X in the equation 2^X + 2 = 66 is 6.
Find the value of a in the equation a/2 / 5/2 = 2
October 28, 2024
To solve for a in the equation (a/2) ÷ (5/2) = 2, first rewrite the division as multiplication by the reciprocal, then multiply the numerators and denominators, simplify the fraction, isolate a by multiplying both sides by 10, and finally solve for a by dividing both sides by 2, resulting in a = 10.
Solve for x in the equation 16/x = x^2/4
October 28, 2024
To solve the equation 16/x = x^2/4, cross-multiply to get 64 = x^3, then take the cube root of both sides to find x = 4.
Solve for x in an equation with an exponent
October 28, 2024
The solution to the equation (1/3)^(x+3) = 9^x is x = -1.
Find the inverse Laplace transform of 1/x^(3/2).
October 27, 2024
The inverse Laplace transform of 1/x^(3/2) is 2/(sqrt(pi))*sqrt(x).
Laplace Transform of sin^2(t)
October 27, 2024
The Laplace transform of sin^2(t) is 2 / (s * (s^2 + 4)).