Simplify the given expression below 7 + 3i²i
To simplify the expression 7 + 3i²i, we start by addressing the term i². Recall that in complex numbers, i is defined as the imaginary unit, where i² = -1. Therefore, we can replace i² in the expression: 7 + 3(-1)i This simplifies further to: 7 – 3i So, the simplified form of the expression […]
In how many different orders can you line up 8 cards on a table?
To determine how many different ways you can line up 8 cards, we need to calculate the number of permutations of the 8 cards. A permutation is an arrangement of objects in a specific order. The formula for permutations of n distinct objects is given by: P(n) = n! Where n! (n factorial) is the […]
Find the Exact Trigonometric Ratios for the Angle x Whose Radian Measure is Given if an Answer is Undefined Enter Undefined 3π/4
The angle x is given in radians as 3π/4. We need to find the exact trigonometric ratios: sine, cosine, and tangent for this angle. Sine Ratio The sine of an angle in the unit circle corresponds to the y-coordinate of the point at that angle. For 3π/4, this angle is located in the second quadrant […]
Find the Exact Length of the Curve y = x^3 – 3x + 4
To find the exact length of the curve defined by the function y = x^3 – 3x + 4, we can use the arc length formula: L = ∫ from a to b √(1 + (dy/dx)²) dx First, we need to find the derivative (dy/dx): dy/dx = 3x² – 3 Next, we need to calculate […]
If f(x) = 1/x^3, what is the derivative of the inverse of f(x)?
To find the derivative of the inverse of a function, we can use the formula: (f-1)'(y) = 1 / f'(x) where y = f(x). From the question, we have: f(x) = 1 / x3. First, we need to find the derivative of f(x): f'(x) = -3 / x4. Next, we need to express x in […]
What is the greatest common factor of 4k, 18k^4, and 12?
To find the greatest common factor (GCF) of the numbers 4k, 18k4, and 12, we first need to identify the factors of each term. 1. **Factors of 4k**: The factors are 4 and k. The number 4 can be broken down into its prime factors as 22. 2. **Factors of 18k4**: The number 18 can […]
Less Than, Greater Than, and Not Not Equal To Are Examples of?
Less than (<), greater than (>), and not not equal to (<>) are examples of comparison operators in programming and mathematics. These operators are used to compare two values or variables. The less than operator (<) checks if the value on the left is smaller than the value on the right. Conversely, the greater than […]
If the diameter of circle C is 3 times greater than the diameter of circle D, how many times greater is the area of circle C compared to circle D?
To find out how many times the area of circle C is compared to circle D, we need to use the formula for the area of a circle, which is A = πr², where r is the radius of the circle. First, let’s denote the diameter of circle D as d. Therefore, the radius of […]
How do you solve the equation 0 = 2 sin(2x) cos(2x) on the interval [0, π]?
To solve the equation 0 = 2 sin(2x) cos(2x), we can start by simplifying it using a trigonometric identity. Recall that sin(2x) = 2 sin(x) cos(x). This allows us to rewrite the equation: 0 = sin(4x) Now we can see that the equation is set to zero, which means we are looking for the angles […]
What is the line containing the points (0, 4) and (3, 2)?
To find the line containing the points (0, 4) and (3, 2), we first need to determine the slope of the line using the formula: Slope (m) = (y2 – y1) / (x2 – x1) Here, the two points are (x1, y1) = (0, 4) and (x2, y2) = (3, 2). Substituting these values into […]