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marissa [1.9K]
3 years ago
12

The line y=5x+b is tangent to the graph y=/x at the point P= (a,/a) Find P and determine b.

Mathematics
1 answer:
Naily [24]3 years ago
8 0
P = (1/100 , 1/10)
b = 1/20
Equate both equations. Use the substitution y=/x (/ means square root). Obtain an equation in terms of y. 5y2 - y + b = 0 Use b2 - 4ac = 0 for tangent. You'll get the answer for b then replace in equation, overall 5y2 - y + 1/20 = 0. Use the quadratic formula to solve for y. You'll obtain y = 1/10 as answer. Using the substitution y=/x, x=y2, x = (1/10)2 = 1/100, /x = 1/10. 5y2 and (1/10)2 are ...to the square....5y to the power of 2.
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Step-by-step explanation

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  • \rightarrow 3A=\begin{bmatrix} 3*6 & 3*6 & 3*4\\\\3*7 & 3(-4) & 3*4\\\\ 3(-6) & 3*9 & 3(-3)\end{bmatrix},\:\: 9B =\begin{bmatrix}9*1 &9* 5 &9( -8)\\\\ 9*9 & 9(-5) & 9(-8)\\\\ 9*9 & 9(-5) & 9*2\end{bmatrix}

  • \rightarrow 3A=\begin{bmatrix} 18 & 18 & 12 \\\\ 21 & -12 & 12\\\\ -18 & 27 & -9\end{bmatrix},\:\: 9B =\begin{bmatrix} 9 & 45 & -72 \\\\ 81 & -45 & -72\\\\ 81 & -45 & 18\end{bmatrix}

  • \rightarrow 3A+9B=\begin{bmatrix}18+9 & 18+45 & 12+(-72) \\\\ 21+81 & -12 +(-45) & 12+(-72)\\\\ -18+81 & 27+(-45) & -9+18 \end{bmatrix}

  • \rightarrow 3A+9B=\begin{bmatrix} 18+9 & 18+45 & 12-72 \\\\ 21+81 & -12 -45 & 12-72\\\\ -18+81 & 27-45 & -9+18 \end{bmatrix}

  • \rightarrow \purple{\bold{3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}}}
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