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3 years ago

How can you find missing angles

1 answer:

5 0

You need to know atleast 2 of three sides from a triangle, or 1 side and 1 angle of a triangle. Then you can use trigonometry to find the angle needed.

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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]

Answer-

(78,104) is the closest to the interior point.

Solution-

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

C) Consider the time 3:40pm where the initial side is the hour hand and terminal side is the

Stells [14]

Answer:

210 degrees
-150 degrees

Step-by-step explanation:

When the time is 3:40pm

The Initial Side (hour hand) is at 3.
Terminal Side (Minute hand) is at 8.

(a)The angle between the two hands in standard position is drawn and attached below.

(b)Now, each hour = 30 degrees

Therefore, the angle between 3 and 8 in an anticlockwise movement

= 7 X 30 =210 degrees

Stating the angle as a negative angle, we have:

$210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ$

7 0

4 years ago

Ricky is at the bakery shop when he sees that 8 pastries cost

BlackZzzverrR [31]

Answer:

320

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The function below show how much Jayna and Hannah charge for babysitting. Which statement best compares the two plants?

Natasha2012 [34]

Answer:

Jayna charges a lower hourly rate

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A box contains 100 colored chips; some are pink and some are blue. Milton chooses a chip at random, records the color, and place

Mademuasel [1]

So milton picked up 30 chips and of these 12 were pink. 12/30 were pink. To make 30 to 100 we multiply by 3.3333. We must also multiply the top number of the fraction as well. So 12*3.333=40 and 30*3.333=100. So you can estimate that the total number of pink chips in the box is 40

7 0

4 years ago