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3 years ago

5

PLEASE HELP URGENT!!!!!!!!!!!!!!!!!!!!!!!!

1 answer:

3241004551 [841]3 years ago

8 0

Answer:

8 bottles of juice.

Step-by-step explanation:

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Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

kondor19780726 [428]

<u>Answer-</u>

<em>(78,104)</em><em> is the closest to the interior point.</em>

<u>Solution-</u>

The equation of the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

As the point will be on the circle, so the coordinate of the point will be,

$(x,\sqrt{16900-x^2})$

The distance "d' between the point and (30,40) is,

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

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Now, we have to calculate x for which d is minimum. d will be minimum when $9400-60x-80\sqrt{16900-x^2}$ will be minimum.

Let,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

Finding the critical values,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

f''(x) is positive, so f(x) will be minimum at x=78

For x = 78, y will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

Therefore, the point is (78,104)

5 0

4 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B2%7D" id="TexFormula1" title="\frac{s}{2}" alt="\frac{s}{2}" align="absmiddle

Olegator [25]

S = 92

Explanation: I just know

4 0

3 years ago

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Elizabeth wants to buy her mother a pair of pearl earrings for Mother’s Day. The earrings cost $50. The sales tax rate is 7.5%.

egoroff_w [7]

Answer:

$53.50

Step-by-step explanation:

7.5 percent of $50 is $3.50.

Then add $50 + $3.50.

$53.50

6 0

2 years ago

They deleted all my questions this is messed up and my point i had over 2000

Lesechka [4]

Answer:

i feel bad

Step-by-step explanation:

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3 years ago

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A horse is 17 hands tall at the hand equals 4 inches how tall is the horse in inches

Lilit [14]

<h3><u>68 inches</u></h3>

Because we know how large each hand is, we can multiply the number of hands by the amount of inches each one represents to find the total number of inches.

17 * 4 = 68

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3 years ago

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