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1 year ago

20 POINTS

Mathematics

1 answer:

Georgia [21]1 year ago

5 0

Answer is in the photo, hope it helps. If you have any questions about the answer, please feel free to ask :)

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The point P(21,35) is on the terminal side of an angle in standard position. What is the distance from P to the origin?

Ira Lisetskai [31]

Answer:

The distance from P to origin is approximately 40.82 units.

Step-by-step explanation:

We are given the following in the data:

The point P(21,35)

We have to find the distance of point P from the origin.

Coordinates of origin: (0,0)

Distance formula:

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

Putting the values, we get,

$(21,35), (0,0)\\\\d = \sqrt{(0-21)^2 + (0-35)^2} = \sqrt{1666} = 7\sqrt{34} \approx 40.82\text{ units}$

The distance from P to origin is approximately 40.82 units.

7 0

3 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

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

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

4 0

3 years ago

Complete the ordered pairs (9,...), (..., 71) for the equation. y= 10X-9

zaharov [31]

Answer:

(9, 81) (8, 71)

Step-by-step explanation:

My explanation is in the picture. All I did was replace the known variable with the proper letter!

4 0

3 years ago

Mrs. Thompson wants to buy centerpieces to use at a party. It will cost $49 to have the centerpieces delivered plus $0.89 per ce

dalvyx [7]

Answer:

49+0.89c

Step-by-step explanation:

This should be the answer good luck :)

8 0

3 years ago

23 ones x 2 tens= answer

Kaylis [27]

The answer is 460
1. 23 ones is the same as 23
2. 2 tens is the same as 20
3. 23 ones x 2 tens is the same as       23
                                                            x20
                                                        ________

Hope you get it and hope i helped!
Buh-Bye

3 0

3 years ago

Read 2 more answers