Answer:
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Step-by-step explanation:
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
![\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%286%2C7%29%20%5C%5C%20B%289%2C9%29%20%5C%5C%20C%288%2C6%29%20%5Cend%7Bgathered%7D)
step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
![\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%286%2C7%29%5Cto%20A%5E%7B%5Cprime%7D%2812%2C14%29%20%5C%5C%20B%289%2C9%29%5Cto%20B%5E%7B%5Cprime%7D%2818%2C18%29%20%5C%5C%20C%288%2C6%29%5Cto%20C%5E%7B%5Cprime%7D%2816%2C12%29%20%5Cend%7Bgathered%7D)
step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
Answer:
11
Step-by-step explanation:
(Note that the diagram is not to scale)
You know BC is 6
You know DC is 5
You know CE is 12
Using K's position, it shows that AC is one off from EC
AC=11
Answer:
2×38. ∴=6 38 4. ∴=34 bag of food.
Step-by-step explanation:
Answer:
![f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-%5Cfrac%7B65%7D%7B2%7Dx%5E%7B%5Cfrac%7B11%7D%7B2%7D%7D%5C%20%2B%5Cfrac%7B49%7D%7B2%7Dx%5E%7B-%5Cfrac%7B9%7D%7B2%7D%7D)
or
![f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-32.5x%5E%7B5.5%7D%5C%20%2B%5C%2024.5x%5E%7B-4.5%7D)
Step-by-step explanation:
Rather than solving this question in a more complex method by directly using the product rule and quotient rule, it can first be considered to perform some algebraic manipulation (index laws) to simplify the expression before taking the derivative.
![\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^6\ \sqrt{x}\ +\ \frac{-7}{x^3\ \sqrt{x}}\\\\f\left(x\right)\ =\ -5x^6\cdot x^{\frac{1}{2}}\ +\ \frac{-7}{x^3\cdot x^{\frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{6\ +\ \frac{1}{2}}\ +\ \frac{-7}{x^{3\ +\ \frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ +\ \frac{-7}{x^{\frac{7}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Blarge%7D%5Cbegin%7Barray%7D%7Bl%7Df%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E6%5C%20%5Csqrt%7Bx%7D%5C%20%2B%5C%20%5Cfrac%7B-7%7D%7Bx%5E3%5C%20%5Csqrt%7Bx%7D%7D%5C%5C%5C%5Cf%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E6%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%20%2B%5C%20%5Cfrac%7B-7%7D%7Bx%5E3%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%5C%5C%5C%5Cf%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E%7B6%5C%20%2B%5C%20%5Cfrac%7B1%7D%7B2%7D%7D%5C%20%2B%5C%20%5Cfrac%7B-7%7D%7Bx%5E%7B3%5C%20%2B%5C%20%5Cfrac%7B1%7D%7B2%7D%7D%7D%5C%5C%5C%5Cf%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E%7B%5Cfrac%7B13%7D%7B2%7D%7D%5C%20%2B%5C%20%5Cfrac%7B-7%7D%7Bx%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%7D%5C%5C%5C%5Cf%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E%7B%5Cfrac%7B13%7D%7B2%7D%7D%5C%20-7x%5E%7B-%5Cfrac%7B7%7D%7B2%7D%7D%5Cend%7Barray%7D)
Now, the derivative of the function can be calculated simply by only using the power rule, which yields
![\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\\\\f^{\prime}\left(x\right)\ =\ \left(-5\right)\left(\frac{13}{2}\right)\left(x^{\frac{13}{2}\ -\ 1}\right)\ -\ \left(7\right)\left(-\frac{7}{2}\right)\left(x^{-\frac{7}{2}\ -\ 1}\right)\\\\f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}\\\\f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}\end{array}\\\end{large}](https://tex.z-dn.net/?f=%5Cbegin%7Blarge%7D%5Cbegin%7Barray%7D%7Bl%7Df%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-5x%5E%7B%5Cfrac%7B13%7D%7B2%7D%7D%5C%20-7x%5E%7B-%5Cfrac%7B7%7D%7B2%7D%7D%5C%5C%5C%5Cf%5E%7B%5Cprime%7D%5Cleft%28x%5Cright%29%5C%20%3D%5C%20%5Cleft%28-5%5Cright%29%5Cleft%28%5Cfrac%7B13%7D%7B2%7D%5Cright%29%5Cleft%28x%5E%7B%5Cfrac%7B13%7D%7B2%7D%5C%20-%5C%201%7D%5Cright%29%5C%20-%5C%20%5Cleft%287%5Cright%29%5Cleft%28-%5Cfrac%7B7%7D%7B2%7D%5Cright%29%5Cleft%28x%5E%7B-%5Cfrac%7B7%7D%7B2%7D%5C%20-%5C%201%7D%5Cright%29%5C%5C%5C%5Cf%5E%7B%5Cprime%7D%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-%5Cfrac%7B65%7D%7B2%7Dx%5E%7B%5Cfrac%7B11%7D%7B2%7D%7D%5C%20%2B%5Cfrac%7B49%7D%7B2%7Dx%5E%7B-%5Cfrac%7B9%7D%7B2%7D%7D%5C%5C%5C%5Cf%5E%7B%5Cprime%7D%5Cleft%28x%5Cright%29%5C%20%3D%5C%20-32.5x%5E%7B5.5%7D%5C%20%2B%5C%2024.5x%5E%7B-4.5%7D%5Cend%7Barray%7D%5C%5C%5Cend%7Blarge%7D)