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To find the value of sin(4x) cos(4x) cot(4x), let’s start by breaking down what each of these terms means and how they relate to each other mathematically. 1. **Understanding the Terms**: sin(4x): This represents the sine of an angle measured in radians or degrees, in this case, 4 times x. cos(4x): This is the cosine … Read more

Solving the Quadratic Equation x² + 5x – 6 = 0 A quadratic equation is usually in the form of ax² + bx + c = 0, where a, b, and c are constants. In our case, the equation is: x² + 5x – 6 = 0 Here, we can identify the coefficients as: a … Read more

In military time, 2 AM is represented as 02:00. The military time system uses a 24-hour clock format, which eliminates the need for AM and PM designations. Here’s a breakdown: In the morning hours, military time ranges from 00:00 to 11:59 which corresponds to 12:00 AM to 11:59 AM in standard time. After 12:00 PM … Read more

The function we are examining is 2 sin(x) cos(x). To find the first and second derivatives, we will apply differentiation rules. Step 1: First Derivative We can use the product rule for derivatives, which states that if you have two functions u and v, the derivative of their product is given by: (u * v)’ … Read more

To determine how long it takes to travel 80 miles at a speed of 80 miles per hour, you can use a simple formula: Time = Distance ÷ Speed In this case, the distance is 80 miles and the speed is 80 miles per hour. Plugging these values into the formula gives: Time = 80 … Read more

The quotient of two numbers is found by dividing one number by the other. In this case, we need to divide 18 by 1000. This can be expressed mathematically as: Quotient = 18 ÷ 1000 Now, performing the division: 18 ÷ 1000 = 0.018 Thus, the quotient of 18 and 1000 is 0.018. This means … Read more

At 270 degrees, which is equivalent to 3π/2 radians, we can determine the values of the six primary trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. 1. Sine Function The sine of 270 degrees is given by: sin(270°) = -1 2. Cosine Function The cosine of 270 degrees is: cos(270°) = 0 3. Tangent … Read more

To find an expression equivalent to 2x² + 2x + 7, we can analyze the polynomial and look for ways to factor or rewrite it. Firstly, let’s rewrite the given expression clearly: 2x² + 2x + 7 We can see that this is a quadratic polynomial in the format of ax² + bx + c, … Read more

To determine the open intervals on which a function is increasing by examining its graph, follow these steps: Understand the Graph: Start by looking at the graph of the function. An increasing function is characterized by a slope that moves upward as you move from left to right. This means that for any two points … Read more

To find the value of 16 to the power of 1/4, we can follow these steps: Understand the Expression: The expression 161/4 indicates we are looking for the fourth root of 16. Identify the Base: 16 can be expressed as a power of 2. Specifically, we know: 16 = 24 Apply the Power Rule: When … Read more