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2 years ago

Write an equation for the orbit of Saturn in the form x^2/a^2 + y^2/b^2 = 1

Mathematics

1 answer:

frozen [14]2 years ago

7 0

Answer:

x²/2166784 +y²/2159989 = 1

Step-by-step explanation:

The relationship between the semi-axes and the eccentricity of an ellipse is ...

e = √(1 -b²/a²)

In order to write the desired equation we need to find 'b' from 'e' and 'a'.

<h3>semi-minor axis</h3>

Squaring the equation for eccentricity gives ...

e² = 1 -b²/a²

Solving for b², we have ...

b²/a² = 1 -e²

b² = a²(1 -e²)

<h3>ellipse equation</h3>

Using the given values, we find ...

b² = 1472²(1 -0.056²) = 2166784(0.996864) ≈ 2159989

The desired equation is ...

x²/2166784 +y²/2159989 = 1

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Simplify. (-2a^7y^4)(4ay^2)

dybincka [34]

Answer:

$-8a^8y^6$

Step-by-step explanation:

<h2><u>Lesson : Simplifying:</u></h2><h2><u /></h2><h2><u /></h2>

Given:

$(-2a^7y^4)(4ay^2)$

"Simplifying"

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$(-2a^7y^4)(4ay^2)$ <em />

<em>Remove the parenthesis</em>

<em>Multiply the numbers</em>

<em>Apply the exponent rule</em>

<em>Add the numbers</em>

<em>Apply the exponent rule once again</em>

<em>Add the numbers once again</em>

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5 0

4 years ago

Find the area of a triangle

schepotkina [342]

Answer:

154 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 (22) * 14

154 cm^2

8 0

3 years ago

Read 2 more answers

A box witxh a height (x+5) cm has a square base with side x com. A second box with height (x+2) com has a square base with side

Eva8 [605]

Answer:

x=5.37 cm

Step-by-step explanation:

we know that

The volume of the box is

$V=Bh$

where

B is the area of the base of the box

h is the height of the box

we have that

The area of the base is

$B=x^2\ cm^2$

$h=(x+5)\ cm$

The volume of the Box 1

is equal to

$V_1=x^2(x+5)\ cm^3$

$V_1=(x^3+5x^2)\ cm^3$

we have that

The area of the base is

$B=(x+1)^2\ cm^2$

$h=(x+2)\ cm$

The volume of the Box 2

is equal to

$V_2=[(x+1)^2(x+2)]\ cm^3$

$V_2=[(x^2+2x+1)(x+2)]\ cm^3$

$V_2=(x^3+2x^2+x+2x^2+4x+2)\ cm^3$

$V_2=(x^3+4x^2+5x+2)\ cm^3$

Equate the equation of Volume 1 to the equation of Volume 2

$(x^3+5x^2)=(x^3+4x^2+5x+2)$

$(5x^2)=(4x^2+5x+2)$

$5x^2-4x^2-5x-2=0$

$x^2-5x-2=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is x=5.37 cm

see the attached figure

8 0

3 years ago

HELP ASAP

sweet [91]

Answer: 2(7x + 3y + 4) [unsimplified] or 14x + 6y + 8 [simplified]

Step-by-step explanation: The perimeter of a parallelogram is 2 * (the two sides.)

Adding 5x + 4 and 2x + 3y, we get 7x + 3y + 4 by combining like terms in the x terms.

Now, we multiply by 2. This is 2(7x + 3y + 4) or 14x + 6y + 8

4 0

2 years ago

The Calm Spa charges annual fee of $125 plus $10 per hour of use. The Relax Spa charges annual dues of $230 plus $7 per hour of

Oksi-84 [34.3K]

Answer:

The total number of hours = 35 hours.

Step-by-step explanation:

The annual fee of Calm Spa = $125

Per hour charge of Calm Spa = $10

Annual fee of Relax Spa = $230

Per hour charge of Relax Spa = $7

Now we have to find the number of hours for which both have same cost.

Let the number of hours = x

Thus, 125 + 10x = 230 + 7x

10x-7x = 230 – 125

3x = 105

x = 35

The total number of hours = 35 hours.

6 0

3 years ago