How do you integrate cot²x dx?
To integrate the function cot²x with respect to x, we can use a standard trigonometric identity and a basic integral rule. First, recall the identity: cot²x = csc²x – 1 This identity allows us to rewrite our integral as follows: ∫cot²x dx = ∫(csc²x – 1) dx Now we can split the integral into two […]
How many different arrangements of 5 letters can be made from the 26 letters of the alphabet?
To determine the number of different arrangements of 5 letters from the 26 letters of the alphabet, we can use the concept of permutations. Since the order of the letters matters (for example, ‘ABCDE’ is different from ‘EDCBA’), we will calculate permutations. The number of ways to arrange ‘n’ items taken ‘r’ at a time […]
What is 5 of 5000?
To find out what 5 of 5000 is, you need to calculate 5% of 5000. This is done by taking 5 divided by 100, and then multiplying the result by 5000. The calculation looks like this: 5% = 5/100 = 0.05 0.05 * 5000 = 250 So, 5 of 5000 is 250. This means that […]
What Are the Figures Having Same Shape and Size Called?
The figures that have the same shape and size are called congruent figures. Congruent figures can be superimposed on each other, meaning that they match exactly when laid on top of one another. For example, two triangles can be considered congruent if all their corresponding sides and angles are equal. This property can be used […]
What is the area of a rhombus with sides of 6 inches and an angle of 60 degrees?
To find the area of a rhombus when the lengths of the sides and one of the angles are known, you can use the formula: Area = a² × sin(θ) where a is the length of a side, and θ is the angle between two sides. In this case, we have: Length of a side […]
What is the square root to the power of 4?
The square root to the power of 4 can be simplified using the properties of exponents. The square root of a number is the same as raising that number to the power of 1/2. Therefore, we can express the square root of a number ‘x’ as: √(x) = x^(1/2) When we raise the square root […]
Which shape has four congruent sides and two sets of parallel sides?
The shape that has four congruent sides and two sets of parallel sides is a square. A square is defined as a quadrilateral (a four-sided figure) with all sides of equal length and all interior angles equal to 90 degrees. The property of having two sets of parallel sides is also characteristic of rectangles, but […]
What is the discriminant of the quadratic equation 3 + 4x + 6x²?
The discriminant of a quadratic equation is a key value that helps to determine the nature of the roots of the equation. For a standard quadratic equation of the form ax² + bx + c = 0, the discriminant (D) is calculated using the formula: D = b² – 4ac In your case, the equation […]
What is the difference between a polygon and a polyhedron?
A polygon is a two-dimensional shape that has straight sides and is formed by connecting a finite number of points. These points, known as vertices, are connected by line segments to create the shape. Common examples of polygons include triangles, squares, and pentagons. In contrast, a polyhedron is a three-dimensional shape that is made up […]
What is the solution of 3x + 5 = 2x + 7?
To solve the equation 3x + 5 = 2x + 7, we need to isolate the variable x. Step 1: Start by getting all the terms involving x on one side and the constant terms on the other side. We can do this by subtracting 2x from both sides: 3x – 2x + 5 = […]