📢 Shares

Solve the equation x^12 = (x-1)^12 for x. The solution is x = 1/2.

Solve the equation (√(A^2-4))/(√(A-3)) = 2 for A. The solution involves squaring both sides, simplifying, and using the quadratic formula to find the complex solutions A = 2 + 2i and A = 2 - 2i.

Calculate the maximum concentrated live load a W18x46 A992 steel beam can support with a 16ft span, lateral support at ends, and a load 4ft from the left support. The bearing lengths are 4 inches at the supports and 8 inches at the load, with 3/4 inch bearing plates. The solution considers bending, shear, web crippling, and local web yielding, resulting in a maximum load capacity of 97.63 kips.

Discover the formula and set builder notation for the sequence 2, 5, 9, 14, 20. Learn how to identify patterns and express them mathematically.

Solve the equation (r-6)^2 + (r-3)^2 = r^2. The solution involves expanding the squares, combining like terms, and solving the resulting quadratic equation. The solutions are r = 15 and r = 3.

This math puzzle presents a pattern where two numbers are combined to produce a third. The pattern is to square each number, then add the results. For example, 2 and 4 become 20 because 2^2 + 4^2 = 20. The puzzle asks for the result of combining 1 and 7, which is 50.

This math puzzle presents a pattern where each number is multiplied by the number one less than itself. Solve for the missing number in the sequence: 8 = 56, 7 = 42, 6 = 30, 5 = 20, 3 = ? The answer is 6.

This problem involves finding the value of x in a triangle where the angles are represented by 2x, 3x, and x. The solution uses the fact that the angles inside a triangle add up to 180 degrees to set up an equation and solve for x. The answer is x = 30.

This math problem asks you to find the area of a blue square inside a larger square. The larger square has sides of 4 units, and the blue square is surrounded by four white triangles. By calculating the area of the larger square and subtracting the area of the four triangles, we find the area of the blue square to be 10 square units.

This math problem asks to find the sum of the areas of two triangles (A and B) within a parallelogram. The parallelogram is divided into four triangles, with two of them having areas of 2 m² and 5 m². The solution uses the fact that the diagonals of a parallelogram divide it into four triangles of equal area. Therefore, the areas of triangles A and B are also 2 m² and 5 m², respectively. The sum of their areas is 2 m² + 5 m² = 7 m². The answer is b. 7 m².

Solve for T in the exponential equation 2^T + 2^(T+1) = 24. The solution reveals T to be 3.

This math puzzle asks you to find a number that gives the same result when added to 1/2 as when multiplied by 1/2. The solution is -1.

Is 9.11 greater than 9.9? Find out the answer and the difference between these two decimal numbers.

This math problem involves finding the measure of an angle (X) in a triangle using the exterior angle theorem. The triangle has one angle of 25 degrees and an exterior angle of 150 degrees. The solution shows that the angle X is 125 degrees.

Solve the equation 2√x - 14 = 288/√x step-by-step using the quadratic formula. The solution is x = 256.

Simplify the nested radical expression √(5 + √11). Using a method involving squaring and the quadratic formula, it's determined that √(5 + √11) cannot be simplified further and remains in its simplest form.

If a/b = 0.25, find the value of 2a + 3b in terms of b. The solution shows step-by-step how to substitute and simplify the expression to get the final answer: 7b/2.

Express sums of Fibonacci numbers in terms of Fibonacci numbers. Find the simplified expressions for sums like F1+F2+...+F15, F1+F3+...+F29, and others, using Fibonacci identities. Solutions include F17-1, F30, and some cases with no simple closed form.

Solve the quadratic equation x² = (20-x)*10/2. The solutions are x = (-5 ± 5√17)/2, approximately x ≈ 8.09 or x ≈ -13.09.

This pre-calculus activity covers identifying conic sections (hyperbola, parabola, circle), proving trigonometric identities (sin(-θ) = -sin θ, csc²θ - cot²θ = 1), and evaluating functions (f(x) = 3x², g(x) = -2x + 7). Solutions are provided step-by-step for each problem.

Simple math problem: 1 + 1 equals 2. Find the solution and understand basic addition with this quick example.

Discover the pattern in the math equations 2^6 x 2^6 = 2^11 + 2^11 and 3^8 x 3^8 = 3^15 + 3^15 + 3^15. Learn how to generalize this pattern and create more examples.

This problem asks to find the value of x^x, given that x = 4^-2. The solution involves simplifying x, applying exponent properties, and calculating the final result, which is 1/√[4]2 or approximately 0.8409.

This math problem involves finding the sum of two angles (x and y) in a triangle. Using the fact that the angles in a triangle add up to 180 degrees and that angles on a straight line add up to 180 degrees, we can solve for x and y. The solution shows that x + y = 118 degrees.

This problem asks to solve for x in the equation 4^(2x-2) * 4^(-4x+1) = 1/16. The solution is x = 1/2.

This math problem asks to solve for A in the equation 2A⁻¹ + 1/2 = 1. The solution is A = 4.

This math problem involves finding the values of x and y in a triangle with angles expressed as algebraic expressions. The solution involves setting up equations based on the angle sum property of triangles and straight lines, and solving for x and y. The solution is x = 30 and y = 100.

This math problem asks to find the value of 'a' given that f(x) = (x-3)² and f(a) = a². The solution involves substituting 'a' into the function, expanding the equation, and solving for 'a'. The answer is a = 3/2 or 1.5.

This math problem involves solving for the ratio A/P given the equation (A+P)/(A-P) = 9/2. The solution involves cross-multiplication, rearranging terms, and expressing A in terms of P to find the value of A/P, which is 11/7.

This problem asks to find the area of a right-angled triangle inscribed in a circle, where the base of the triangle is the diameter of the circle. The diameter is given as 12 cm. The solution uses the formula for the area of a triangle and the fact that the height of the triangle is equal to the radius of the circle. The final answer is 36 cm².