Tutor profile: Jenna T.
If we are given that: sin(x) = 12x cos(x) = 6 Then what is tan(x)?
We know that tan(x) = sin(x) / cos(x). So, we can simply plug our values in and simplify as much as possible. tan(x) = 12x / 6 After simplifying, we find that tan(x) = 2x.
Find the derivative of: 5x^3 + 7x^2 + 9x + 1007.
For this question, we can use the power rule! We know that if we are taking the derivative of a term x^n, the result is nx^(n-1). So, for the first term 5x^3, our n is 3. We bring the 3 down to the front, and get (3)(5)x^2. 3 times 5 is 15, so our first term's derivative is 15x^2. For the second term, we repeat. We bring the 2 down to the front, and get (2)(7)x^1. 2 times 7 is 14, and x^1 is just x. So, our second term's derivative is 14x. For the third term, we repeat. Bring the exponent of 1 down to the front, and we get (1)(9)x^0. 1 times 9 is 9, and x^0 is just 1. So, our third term's derivative is 9. For the fourth term, the derivative of any constant is 0, so this disappears from our answer. The final derivative is 15x^2 + 14x + 9.
If: x + x + x = 9 y - z = 8 y + z = 28 Then what is x + y + z?
Our goal here is to determine exactly what x, y, and z are equal to. Once we know that, then we can solve for x + y + z. We first look at our equations. We know x + x + x = 9, which we can write as 3x = 9. Then, we can divide by 3 on both sides of the equal sign, and we then determine that x = 3! Unfortunately, our next two equations don't include x at all. We don't know what y or z is, so we need to cancel out one of those variables. Since y - z = 8, if we add z to both sides, we see that y = 8 + z. So, let's take this and plug it in our third equation for y. That is, since y is 8 + z, let's place that where the y is. y + z = 28 ----> (8 + z) + z = 28. Once we combine like terms, we get 8 + 2z = 28. Now we can solve for z! Subtract 8 from both sides, and get 2z = 20. Then, we divide by 2 on both sides, and we find that z = 10! Now we know that x = 3 and z = 10. Let's solve for y! Plug z in one of your equations and find y. I'll do the second equation: y - z = 8 ----> y - 10 = 8. Add 10 to both sides, and we get y = 18! So, x = 3, y = 18, and z = 10. Therefore, x + y + z ---> 3 + 18 + 10 = 31!
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