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Scorpion4ik [409]

2 years ago

6

step right up for a new brainiest fair answer the question you get right you win the glorious brainiest

1 answer:

olga nikolaevna [1]2 years ago

3 0

Answer:

Mean → <u><em>9</em></u>

Median → <u><em>7</em></u>

Mode → <u><em>4</em></u>

Step-by-step explanation:

For mean ↓

(9+4+17+4+7+8+14) ÷ 7 = <u><em>9</em></u>

For median ↓

G U E S S E D

For mode ↓

Mode is <u><em>4</em></u> because it is shown twice in the data.

2 x 2 = <u><em>4</em></u>

Hope this helped! :^)

⭐Brainliest will be appreciated!⭐

✉️Message me if you have any more questions!✉️

- ✨<u><em>7272033Alt</em></u>✨

Submitted on 4/14/2022 at 6:31 PM

(To avoid plagarism, by users whom decide to copy.)

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ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

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So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

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Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

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$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

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cluponka [151]

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