If fx log3 x 1 What is f 12?
To solve for f(12), we start by understanding the equation given: f(x) = log3 x. The equation tells us that f(x) is defined as the logarithm of x to the base 3. Now, we need to find out what f(12) is, which means we need to calculate log3 12. To calculate log3 12, we can […]
Given the parent functions f(x) = 5x + 1 and g(x) = 3x + 9, what is g(x) – f(x)?
To find g(x) – f(x), we first need to write out both parent functions: f(x) = 5x + 1 g(x) = 3x + 9 Now, we will substitute these expressions into the equation: g(x) – f(x) = (3x + 9) – (5x + 1) Next, we simplify this by distributing the negative sign and combining […]
Find the general solution of the given differential equation: x dy/dx + y = x^2 sin(x)
To find the general solution of the differential equation x dy/dx + y = x^2 sin(x), we start by rearranging the equation: dy/dx + (y/x) = x sin(x) This is a first-order linear ordinary differential equation, which can be solved using the integrating factor method. First, we identify the integrating factor, μ(x), given by: μ(x) […]
Find the next three terms of the sequence 8, 24, 72, 216
To find the next three terms in the sequence 8, 24, 72, 216, we first need to examine how the terms are related to each other. We can look at the ratios between consecutive terms: 24 / 8 = 3 72 / 24 = 3 216 / 72 = 3 From this observation, we can […]
Is the equation x^9 + 5x^3 + 6 = 0 quadratic in form? Explain why or why not.
The equation x9 + 5×3 + 6 = 0 is not quadratic in form. A quadratic equation is typically expressed in the standard form of ax2 + bx + c = 0, where the highest exponent of the variable (x) is 2. In this equation, the term with the highest exponent is x9, which clearly […]
What are the zeros of the quadratic function f(x) = 2x² + 10x + 3?
To find the zeros of the quadratic function f(x) = 2x² + 10x + 3, we need to set the function equal to zero and solve for x: 2x² + 10x + 3 = 0 We can use the quadratic formula x = (-b ± √(b² – 4ac)) / (2a), where a, b, and c […]
Find the LCM of the Following Numbers in Which One Number is the Factor of Other: 520, 618, 1248, 945. What Do You Observe in the Result Obtained?
To find the least common multiple (LCM) of the given numbers 520, 618, 1248, and 945, we first need to understand a few points about LCM. The LCM of a set of numbers is the smallest number that is a multiple of each of the given numbers. When one number is a factor of another, […]
In one day how many times do the minute hand and the second hand of a clock make a straight line?
The minute hand and the second hand of a clock make a straight line with each other 118 times in one day. To understand why, let’s break it down. The second hand completes one full revolution every 60 seconds, while the minute hand takes 60 minutes for one complete cycle. Because the second hand revolves […]
What number is one fifth of one fourth of one ninth of 900?
To find the number that is one fifth of one fourth of one ninth of 900, we will break this down step by step. First, we need to calculate one ninth of 900: One ninth of 900 is 900 ÷ 9 = 100. Next, we find one fourth of this result: One fourth of 100 […]
Find the Centroid of the Region Bounded by the Curves y = x³, y = 10, and y = 0
To find the centroid of the region bounded by the curves y = x³, y = 10, and y = 0, we first need to determine the points of intersection of these curves. The equation y = x³ intersects y = 10 when: x³ = 10 Taking the cube root of both sides gives us: […]