Find the sum of 4i and 10 + 5i
To find the sum of the complex numbers 4i and 10 + 5i, we start by identifying the real and imaginary parts of each number. The first number, 4i, can be expressed as: Real part: 0 Imaginary part: 4 The second number, 10 + 5i, has: Real part: 10 Imaginary part: 5 Now, we can […]
Find the radian measure of the central angle of a circle with radius 90 inches that intercepts an arc of length 130 inches
To find the radian measure of the central angle in a circle, we can use the formula: θ = s / r Where: θ is the central angle in radians. s is the length of the arc. r is the radius of the circle. In this case, we have: s = 130 inches r = […]
What is the equation of a horizontal line that passes through the point (2, 2)?
A horizontal line will have the same y-coordinate for all points on that line. In this case, the line passes through the point (2, 2), which means the y-coordinate is 2. The equation of a horizontal line can be written in the form y = b, where b is the y-coordinate. Since our line passes […]
What is the range of the function fx = x^4 – 4x^2?
To determine the range of the function f(x) = x4 – 4×2, we can start by rewriting the function for clarity: f(x) = x2(x2 – 4) Next, we can factor the quadratic part of the function: f(x) = x2(x – 2)(x + 2) This function is a quartic polynomial, and to find the range, we […]
The slope of a line is m; what is the slope of a line perpendicular to this line?
When you have a line with a slope of m, a line that is perpendicular to it will have a slope that is the negative reciprocal of m. This means that if you multiply the slopes of the two lines together, you will get -1. To find the slope of the perpendicular line, you can […]
Find the Number of Sides in a Regular Polygon if Each Interior Angle is 160° or 150°
To find the number of sides in a regular polygon based on its interior angle, we can use the formula: Interior Angle = ((n – 2) × 180) / n where n is the number of sides of the polygon. 1. When the interior angle is 160°: Let’s set the interior angle to 160°: 160 […]
How do we use inequality symbols to compare the numbers 3, 7, 10, and 2?
To compare the numbers 3, 7, 10, and 2 using inequality symbols, we first need to understand what these symbols mean: < means ‘less than’ > means ‘greater than’ <= means ‘less than or equal to’ >= means ‘greater than or equal to’ Now, let’s arrange the numbers in ascending order: 2, 3, 7, and […]
Find the General Solution of the Given Second Order Differential Equation 2y y’
To solve the differential equation of the form 2y y’ = 0, we can start by breaking it down into its factors. Here, the equation can be rewritten as: 2y = 0 or y’ = 0 1. **Solving the first factor:** From 2y = 0, we can conclude that: y = 0 This gives us […]
What is the correct simplification of the expression 4 over y to the power of negative 3?
To simplify the expression \( \frac{4}{y^{-3}} \), we need to remember that dividing by a negative exponent is equivalent to multiplying by the positive exponent. First, we can rewrite the expression as follows: \( \frac{4}{y^{-3}} = 4 \times y^{3} \) This is because moving \( y^{-3} \) from the denominator to the numerator changes the […]
What is the circumference and area of a circle with a radius of 4 meters?
To find the circumference and area of a circle, we use two important formulas: Circumference: C = 2 × π × r Area: A = π × r² Where C is the circumference, A is the area, r is the radius, and π (pi) is approximately 3.14. Given a radius (r) of 4 meters, we […]