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BartSMP [9]
3 years ago
12

The orbit of Pluto can be modeled by the equation {x^2}/{39.5^2} + {y^2}/{38.3^2 } = 1, where the units are astronomical units.

Suppose a comet is following a path modeled by the equation x = y^{2} + 20. What are the points of intersection of the orbits of Pluto and the comet? (Not necessarily where they'll hit each other, just where the paths they take cross each other.)

Mathematics
1 answer:
Alex17521 [72]3 years ago
5 0

9514 1404 393

Answer:

  (39.24, -4.386), (39.24, 4.386)

Step-by-step explanation:

A graphing calculator solves this easily.

__

For an algebraic solution, you can substitute for y^2. To avoid messing with large numbers, we define p=39.5^2 and q=38.3^2. Then after substitution for y^2, we have ...

  x^2/p +(x-20)/q = 1

Multiplying by pq gives ...

  qx^2 +px -20p = pq

  qx^2 +px -20p -pq = 0

  x = (-p +√(p^2 +4qp(p+q)))/(2q)

Putting the numbers back into this equation gives ...

  x ≈ 39.2401

  y = ±√(x -20) = ±4.38635

The crossing points are (39.2401, ±4.38635).

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5 Find 6 in Surface Area​
iVinArrow [24]

Answer:

8 x 6 = 48

48 divided by 2 = 24

24 x 2 = 48

10 x 12 = 120

120 x 2 = 240

8 x 12 = 96

Add all given areas:

48 + 96 + 240 = 384 in2 is your answer.

3 0
2 years ago
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7 0
3 years ago
(2 x 106) x (0.00009) = ?
RSB [31]

I think you meant to write

(2 × 10⁶) × 0.00009

First, convert 0.00009 to scientific notation:

0.00009 = 9 × 10 ⁻⁵

Then

(2 × 10⁶) × 0.00009 = (2 × 10⁶) × (9 × 10 ⁻⁵)

… = (2 × 9) × (10⁶ × 10 ⁻⁵)

… = 18 × 10¹

… = 1.8 × 10²

4 0
2 years ago
Marsha gave the cashier $20 to pay for 3 pairs of socks the cashier gave her $5.03 in change. each pair of socks cost the same a
eduard

Answer:

$4.99

Step-by-step explanation:

20-5.03=14.97

14.97/3=4.99

5 0
3 years ago
What is the approximate area that is shaded red?
Mashcka [7]

To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.


Area of a rectangle:

A = l × w             [ l = 11 in ; w = 6in ]    Plug these numbers into the equation

A = 11 · 6

A = 66 in²


Area of a triangle:

A=\frac{1}{2}bh     [ b = 4 in ; h = 6 in ] Plug these #s into the equation

A = \frac{1}{2}(4)(6)

A=\frac{24}{2}

A = 12 in²


Area of rectangle - Area of triangle = Area of the shaded region

66 in² - 12 in ² = 54 in²


Your answer is B

3 0
3 years ago
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