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3 years ago

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(Please help)select the number line that represents all solutions of…

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Goshia [24]3 years ago

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Answer:

D olmalı diğerleri yanlış

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Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

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

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

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

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

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

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

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

$y = \frac{\sqrt {10}}{\sqrt 4}$

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

Hence:

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

3 0

3 years ago

ozzi

Hope this helps, I searched it up for you

6 0

2 years ago

Solve the equation for y<br> y +5=-(x – 3)

goldenfox [79]

Answer:

y=-x-2

Step-by-step explanation:

y+5=-(x-3)

y+5=-x+3

y=-x+3-5

y=-x-2

6 0

2 years ago

Read 2 more answers

Your boss tells you that she knows the length of the widgets your company makes is normally distributed with a mean of 25 inches

sp2606 [1]

Answer:

Mean of sampling distribution = 25 inches

Standard deviation of sampling distribution = 4 inches

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 25 inches

Standard Deviation, σ = 12 inches

Sample size, n = 9

We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.

a) Mean of the sampling distribution

The best approximator for the mean of the sampling distribution is the population mean itself.

Thus, we can write:

$\bar{x} = \mu = 25\text{ inches}$

b) Standard deviation of the sampling distribution

$s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{12}{\sqrt{9}} = 4\text{ inches}$

8 0

3 years ago

Dentify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest percent.

love history [14]

Answer:

Step-by-step explanation:

The difference is 130-150 = -20, a decrease.

-20/150 ≅ -0.133, a decrease of 13.3%

4 0

3 years ago