How do I find an equation of the tangent line to the curve at the point (2, 4) for the curve defined by y = 4x – 3x²?
To find the equation of the tangent line to the curve defined by the equation y = 4x – 3x² at the point (2, 4), we need to follow a few steps: Differentiate the curve: We first calculate the derivative of the function, which gives us the slope of the tangent line. The derivative of […]
How do you write a decimal as a fraction?
To write a decimal as a fraction, follow these steps: Identify the decimal: For example, let’s take 0.75. Count the decimal places: The number 0.75 has two decimal places. Convert to fraction: Write the decimal without its decimal point as the numerator (75) over a denominator that is a power of 10. Since 0.75 has […]
How could you check the answer to 27 + 15 + 12 using addition?
To check the sum of 27, 15, and 12 using addition, you should start by adding the numbers together in a step-by-step manner. First, add the first two numbers: 27 + 15 = 42 Next, take this result and add the third number: 42 + 12 = 54 Therefore, by performing the addition step by […]
What is the Formula for Cotangent of Angle A and Angle B?
The formula for cotangent of the addition of two angles A and B is given by: cot(A + B) = (cot A * cot B – 1) / (cot A + cot B) This formula helps to find the cotangent of the sum of two angles using the cotangents of the individual angles. Cotangent is […]
What is a Corollary in Mathematics?
A corollary is a statement that follows readily from a previously proven statement, such as a theorem. It typically derives from the conclusion of that theorem and requires minimal additional proof. For example, if a theorem states that all angles in a triangle sum up to 180 degrees, a corollary might be that in an […]
Find cot x if sin x cot x csc x = √2
To find cot x given the equation sin x cot x csc x = √2, we can start by using the definitions of the trigonometric functions involved. First, we know that: csc x is defined as 1/sin x cot x is defined as cos x/sin x Substituting these definitions into the equation: sin x (cos […]
You purchased a shirt for $850. There is a 6% sales tax. What will be your total cost?
To calculate the total cost of the shirt, we first need to determine the amount of sales tax applied to the purchase. The sales tax is calculated as follows: Sales Tax = Price of Shirt × Sales Tax Rate Sales Tax = $850 × 0.06 = $51 Next, we add the sales tax to the […]
How do you write an equation in slope intercept form for a line with points (3, 1) and (2, 5)?
To write an equation in slope-intercept form, which is expressed as y = mx + b, we first need to determine the slope (m) of the line that passes through the two given points: (3, 1) and (2, 5). The formula for the slope (m) between two points (x1, y1) and (x2, y2) is: m […]
Combine Like Terms: What is a Simpler Form of the Expression 3 + 4y + 3 + 7y?
To simplify the expression 3 + 4y + 3 + 7y, we start by combining the like terms. Like terms are terms that have the same variable raised to the same power. In this expression, we can see that: The constant terms are 3
For the absolute value function f(x) = |x|^2, what is the domain of the function?
The domain of the function f(x) = |x|^2 includes all real numbers. This is because the absolute value function, |x|, is defined for every real number, and raising any real number (including the value of |x|) to the power of 2 is also defined for all real numbers. To elaborate, for any value of x, […]