What is the equation of the line that passes through (1, 5) and (2, 14) in slope-intercept form?
To find the equation of the line that passes through the points (1, 5) and (2, 14), we first need to determine the slope (m) of the line using the formula: m = (y2 – y1) / (x2 – x1) In our case, (x1, y1) is (1, 5) and (x2, y2) is (2, 14). Plugging […]
How do you use logarithmic differentiation to find the derivative of the function y = x^3 + 22x^4 + 44?
To find the derivative of the function y = x^3 + 22x^4 + 44 using logarithmic differentiation, we start by taking the natural logarithm of both sides: ln(y) = ln(x^3 + 22x^4 + 44) Next, we can differentiate both sides with respect to x. Remember to apply the chain rule on the left side: 1/y […]
Find the slope of the line that passes through the pair of points (1, 7) and (10, 1)
Given the function f(x) = 2x² + 4x + 7, find f(4)
To find f(4), we need to substitute x with 4 in the function f(x) = 2x² + 4x + 7. Here are the steps to calculate it: Substitute x with 4 in the function: f(4) = 2(4)² + 4(4) + 7 Calculate (4)²: f(4) = 2(16) + 4(4) + 7 Multiply: f(4) = 32 + […]
Identify the Surface with the Given Vector Equation r(s,t) = (s sin(9t), s^2, s cos(9t))
The given vector equation can be analyzed to identify the surface it represents. The equation is: r(s,t) = (s sin(9t), s^2, s cos(9t)) To understand the surface, we start by examining the components of the vector: The first component is x = s sin(9t). The second component is y = s^2. The third component is […]
How to Add and Subtract Integers Without a Number Line
Adding and subtracting integers can be straightforward once you understand the rules that govern these operations. Here’s how you can do it without using a number line. Adding Integers When adding integers, the process differs based on whether the numbers are positive or negative: If both integers are positive, simply add the numbers together. For […]
If sx = x + 7 and tx = 4x^2 – 3, which expression is equivalent to tsx?
To find an expression equivalent to tsx, we first need to understand what tsx represents. This means we will need to multiply t by sx. We know that: sx = x + 7 tx = 4x^2 – 3 Now, substituting sx into the expression tsx: tsx = t(sx) = t(x + 7) Next, we substitute […]
What is the HCF of the smallest prime number and the smallest composite number?
The smallest prime number is 2, and the smallest composite number is 4. To find the Highest Common Factor (HCF) of these two numbers, we need to identify their factors. The factors of 2 are: 1, 2 The factors of 4 are: 1, 2, 4 The common factors of 2 and 4 are: 1, 2. […]
How to Make a Greater Than or Equal To Sign
To create a greater than or equal to sign (≥), there are a few methods depending on where you want to use it. If you’re typing in a word processor like Microsoft Word, you can insert the symbol by going to the ‘Insert’ tab, then clicking on ‘Symbol’, and finding it in the list, or […]
What will be the total expenditure if the wall paper costs Rs 60 per square metre?
To calculate the total expenditure on wallpaper, you first need to determine the area that needs to be covered in square metres. The cost of wallpaper is given as Rs 60 per square metre, so the total cost will depend on how many square metres you need to cover. Here’s the formula you would use: […]