Answer:
![= 9a^3b^2](https://tex.z-dn.net/?f=%20%3D%209a%5E3b%5E2%20)
Step-by-step explanation:
![\sqrt[3]{-729a^9b^6} =](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-729a%5E9b%5E6%7D%20%3D)
![= ((-9)^3a^9b^6)^{\frac{1}{3}](https://tex.z-dn.net/?f=%20%3D%20%28%28-9%29%5E3a%5E9b%5E6%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%20)
![= (-9)^{3 \times \frac{1}{3}} \times a^{9 \times \frac{1}{3}} \times b^{6 \times \frac{1}{3}}](https://tex.z-dn.net/?f=%3D%20%28-9%29%5E%7B3%20%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%7D%20%5Ctimes%20a%5E%7B9%20%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%7D%20%5Ctimes%20b%5E%7B6%20%5Ctimes%20%5Cfrac%7B1%7D%7B3%7D%7D)
![= (-9)^{1} \times a^{3} \times b^{2}](https://tex.z-dn.net/?f=%20%3D%20%28-9%29%5E%7B1%7D%20%5Ctimes%20a%5E%7B3%7D%20%5Ctimes%20b%5E%7B2%7D%20)
![= -9a^3b^2](https://tex.z-dn.net/?f=%20%3D%20-9a%5E3b%5E2%20)
-3 because you could eliminate the 3x by subtracting it by 3x
9514 1404 393
Answer:
a) 12
b) y +5 = 12(x +2)
Step-by-step explanation:
The slope of a function is its derivative.
a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...
m = 3(-2)^2 = 12 . . . . slope at (-2, -5)
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b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)
<u>Answer-</u>
![f(2)= 6x^4-10x^3+40x-50=46](https://tex.z-dn.net/?f=f%282%29%3D%206x%5E4-10x%5E3%2B40x-50%3D46)
<u>Solution-</u>
The given function is,
![\Rightarrow f(x)= 6x^4-10x^3+40x-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%28x%29%3D%206x%5E4-10x%5E3%2B40x-50)
Now, we have to find the value of f(x) at x=2 i.e f(2), so putting x as 2 in the given function,
![\Rightarrow f(2)= 6(2)^4-10(2)^3+40(2)-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%206%282%29%5E4-10%282%29%5E3%2B40%282%29-50)
![\Rightarrow f(2)= (6\times 16)-(10\times 8)+(40\times 2)-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%20%286%5Ctimes%2016%29-%2810%5Ctimes%208%29%2B%2840%5Ctimes%202%29-50)
![\Rightarrow f(2)= (6\times 16)-(10\times 8)+(40\times 2)-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%20%286%5Ctimes%2016%29-%2810%5Ctimes%208%29%2B%2840%5Ctimes%202%29-50)
![\Rightarrow f(2)= 96-80+80-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%2096-80%2B80-50)
![\Rightarrow f(2)= 96-50](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%2096-50)
![\Rightarrow f(2)= 46](https://tex.z-dn.net/?f=%5CRightarrow%20f%282%29%3D%2046)
Therefore, f(2) was found to be 46.
1, 3, 5 are functions because they pass the vertical line test