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3 years ago

Use the midpoint formula to find the midpoint between H(3, 9) and J(9, -2).

Mathematics

1 answer:

TiliK225 [7]3 years ago

3 0

Hello!

The midpoint formula is basically an average of x and y.

It is also written as: $(\frac{x_{1}+x_{2}} {2},\frac{y_{1}+ y_{2}} {2})$ .

With the formula above, we can substitute the given points into the equation, and simplify.

$(\frac{3 +9}{2}, \frac{9+(-2)}{2}) = (\frac{12}{2}, \frac{7}{2}) = (6, 3.5)$

Therefore, the midpoint between points H and J is choice D, (6, 3.5).

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Determine the location and values of the absolute maximum and absolute minimum of given function: f(x)= ( -x+2)^4, Where 0<=x

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Answer:

The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

Step-by-step explanation:

First, we obtain the first and second derivatives of the function by chain rule and derivative for a power function, that is:

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Second derivative

$f''(x) = 12\cdot (-x + 2)^{2}$

Then, we proceed to do the First and Second Derivative Tests:

First Derivative Test

$-4\cdot (-x+2)^{3} = 0$

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Second Derivative Test

$f''(2) = 12\cdot (-2+2)^{2}$

$f''(2) = 0$

The Second Derivative Test is unable to determine the nature of the critical values.

Then, we plot the function with the help of a graphing tool. The absolute maximum and the absolute minimum are (0, 16) and (2, 0).

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$\bf \qquad \qquad \textit{direct proportional variation}
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\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
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