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
To find the value of 20 divided by 10, you can use the basic principle of division, which essentially asks how many times does 10 fit into 20. The calculation is straightforward: you divide 20 by 10, which you can write as: 20 ÷ 10 Now, performing the division: 20 ÷ 10 = 2 This … Read more
To convert the improper fraction 31/6 into a mixed number, you need to follow a few simple steps: Divide the numerator by the denominator: Divide 31 by 6. When you do this, you find that 31 ÷ 6 = 5 with a remainder of 1. Write down the whole number: The result of the division … Read more
When we talk about 4 raised to the power of 2, we’re actually referring to a mathematical operation known as exponentiation. In this case, 4 is the base and 2 is the exponent. This means that we multiply the base (4) by itself as many times as indicated by the exponent (2). So, calculating 4 … Read more