devyy The derivative of the tangent function, denoted as tan(x), is a fundamental concept in calculus, especially for those working in fields that involve trigonometric functions. The derivative of tan(x) can be derived from the definition of the tangent function itself: tan(x) = sin(x) / cos(x) To find the derivative, we can apply the quotient rule. … Read more
When we talk about 10 raised to the power of 23, we’re referring to a mathematical expression that represents 10 multiplied by itself 22 more times. In numerical terms, this is expressed as: 1023 = 10,000,000,000,000,000,000,000 This number is often written in scientific notation as 1 x 1023. It is a large number frequently used … Read more
To calculate the sale price of an item, you take the original price and subtract the discount amount from it. In this case, the original price of the item is $35, and the discount is $20. The calculation would look like this: Sale Price = Original Price – Discount Plugging in the numbers: Sale Price … Read more
To find the length of a rectangle when you have the area, you’ll need to use the formula for the area of a rectangle: Area = Length × Width If you know the area and the width of the rectangle, you can rearrange this formula to solve for the length: Length = Area ÷ Width … Read more
To find the 7th term of the geometric sequence where the first term (a1) is 1024 and the fourth term (a4) is 16, we can follow these steps: A geometric sequence is characterized by a constant ratio r between successive terms. The nth term of a geometric sequence can be expressed as: an = a1 … Read more
To find the value of cos(120^ ext{°}), we can use the unit circle and some trigonometric identities. First, recognize that 120^ ext{°} is in the second quadrant of the unit circle. In this quadrant, the cosine value is negative. To find the cosine of 120^ ext{°}, we can relate it to a reference angle. The … Read more
The volume of a prism can be calculated using a simple formula that relates to the area of its base and its height. The formula is: Volume (V) = Base Area (B) × Height (h) To elaborate, here’s how it works: Base Area (B): This represents the area of the base of the prism. The … Read more
To find the nth term of the sequence 15, 12, 9, 6, we first need to identify the pattern in the numbers. Let’s analyze the sequence: 15 (1st term) 12 (2nd term) 9 (3rd term) 6 (4th term) We can observe that each term in the sequence is decreasing by 3: 15 – 12 = … Read more
To simplify the expression 2/x² + x – 1/x, we first need to find a common denominator. The common denominator for the terms in the expression is x². We will rewrite each term with this common denominator. The first term, 2/x², already has the denominator x². The second term, x, can be rewritten with the … Read more
To factor the expression 8x² + 12x, we will follow a systematic approach. Here’s how you can do it: Identify the Greatest Common Factor (GCF): The first step in factoring is to find the GCF of the coefficients and the variable terms. In this case, the coefficients are 8 and 12. The GCF of 8 … Read more