Find the 50th term of the sequence 5, 2, 9, 16
To find the 50th term of the sequence, we first need to identify the pattern. The sequence given is: 5, 2, 9, 16. Let’s look at the differences between the consecutive terms: 2 – 5 = -3 9 – 2 = 7 16 – 9 = 7 It seems complicated at first, but if we […]
What is the total surface area of a cuboid with dimensions in the ratio 5:2:1 and a volume of 1250 cubic meters?
To find the total surface area of the cuboid, we need to first determine its dimensions based on the given volume. Let the dimensions of the cuboid be represented as 5x, 2x, and x, where x is a common multiplier. The volume of a cuboid is calculated as: Volume = Length × Breadth × Height […]
What is the probability of an event A that is certain to occur?
The probability of an event that is certain to occur is 1. This means that if you know an event will happen without any doubt, its probability can be expressed as the ratio of favorable outcomes to the total outcomes. In this case, since there are no unfavorable outcomes (the event will definitely happen), the […]
What Are the Zeros of the Function?
The zeros of a function are the values of the variable that make the function equal to zero. In simpler terms, if you input these values into the function, you will get an output of zero. For example, consider the function f(x) = x² – 4. To find the zeros, we need to solve the […]
Is the line y = 3x + 7 parallel or perpendicular to 3x + 9y = 9?
To determine whether the lines are parallel or perpendicular, we first need to find their slopes. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope. Let’s start with the first line: 1. First Line: y = 3x + 7 From this equation, we […]
How Do You Find the Area of an Irregular Shape?
To find the area of an irregular shape, there are several methods you can use depending on the nature of the shape and the tools available to you. Here’s a simple step-by-step method that can work for most irregular shapes: Divide the Shape: Start by breaking the irregular shape into smaller, regular shapes like rectangles, […]
For What Interval Is the Value of f(g(x)) Negative?
To determine the interval where the value of f(g(x)) is negative, we need to analyze both functions, f and g. Start by identifying the domain of g(x) and evaluating what values it can take. Then, plug these values into the function f. The goal is to find out where the output of f(x) is less […]
In how many ways can the letters in the word balloon be arranged?
The word “balloon” consists of 7 letters where certain letters are repeated. Specifically, we have: b: 1 time a: 1 time l: 2 times o: 2 times n: 1 time To find the number of distinct arrangements of the letters in the word “balloon,” we can use the formula for permutations of a multiset: P(n; […]
How to Evaluate the Integral of log(x) / (x^2 + 1) dx?
To evaluate the integral ∫ (log(x) / (x^2 + 1)) dx, we can use integration by parts. Let: u = log(x) (which will differentiate to du = (1/x) dx) dv = 1/(x^2 + 1) dx (which integrates to v = tan-1(x)) Now, by the integration by parts formula ∫ u dv = uv – ∫ […]
Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3?
To find the value of 27 raised to the power of 1/3, we’re looking for the cube root of 27. The cube root of a number is the value that, when multiplied by itself twice (three times total), gives the original number. Let’s break down the steps: Identify the number: We are working with the […]