Tutor profile: Hania F.
convert 123º to radians
Recall that 360º = 2π rads. Therefore, if we use this ratio, we can find the equivalent degrees in radians, 123º/360º = x rads/ 2π rads, solving for x we get the following : 1. 123 x 2π = 246 π 2. 246π/360 = 41π/60 rads
Find the derivative of the following function: f(x) =16 sin(x) + 2x + 3
Derivative means to find the slope or the rate of change of a given function. The given equation is composed of 3 parts: 16 sin(x), 2x. and 3 To find the derivative of 16 sin(x), we first have to look at the derivative of sin(x). The derivative for sin(x) is cos(x), and since we know that 16 is a constant, we can leave it as it is and obtain the following derivative for 16 sin(x) : 16cos(x) To find the derivative of 2x, we know that 2 is a constant so we can apply the known formula for a constant with x, d/dx (cx) = c. From this formula, we can get the following derivative of 2x: 2. Finally, for 3, which is a constant in this case, we can see that for any value of x the value would always remain 3. Meaning, there wouldn't be a "change" in the value since it'll always be constant. Therefore, the derivative of 3 is 0. Putting the parts all together, we obtain the answer: f'(x) = 16cos(x)+2 Note: f'(x) is simply a mathematical way of saying that this is the derivative of f(x)
Suppose that you have the following equation: 2x + Tx = 3. For what values of the constant T does this equation have one solution?
Before first attempting to solve this question, it is necessary to understand what the question is asking. T is a constant in this equation and we want to figure out how we can find the values of T that can give us a number for x and what value wouldn't allow us to get an appropriate value for x. 1. First, we begin by isolating x so that we can get all the x on one side and T on the other: Since we notice that we have x being present two times in the equation, we factor it out and get : x(2+T )=3 isolating for x we get: x=3/(2+T) 2. Notice how there can be an error in the above equation if we have a -2 for T. We can never divide by a 0, therefore if T is equal to -2, this would be a math error. 3. The answer to this question would be that the given solution has a solution for all the values of T except for when it is equal to -2.
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