Answer:
3031081 / 40678884
Step-by-step explanation:
To solve this, we can find the surface area of the moon and Earth, and then see how much the moon covers the Earth. The surface area of a sphere is equal to 4πr², so the radius of the Earth is
4πr² = 4 * π * 6378²
and the radius of the moon is
4πr² = 4 * π * 1741²
To figure out how much of the Earth's surface that the moon covers, we can implement a ratio of moons:Earth. This will give us an understanding of how many moons go inside one Earth. We thus have
(4 * π * 1741²) : ( 4 * π * 6378²) = (4 * π * 1741²) / ( 4 * π * 6378²)
cross out the 4 * π in the numerator and denominator
1741²/6378²
Next, we want to make the denominator 1, as that gives us 1 Earth. To do this, we can divide both the numerator and denominator by 6378². Because we are applying the same expression to both the numerator and denominator, this is essentially multiplying the fraction by 1, keeping it the same. We thus have
(1741²/6378²)/(6378²/6378²)
≈0.0745/1
≈ 0.0745
To put this in a fraction, we would have
(1741²/6378²)/1
= (1741²/6378²)
= 3031081 / 40678884
Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.
Suppose we have 2 positive integers, a and b, then:
gcd (a, b) = the greatest common divisor = common prime factors of a and b
lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b
In the given problem:
gcd (a, b) = 15
prime factorization of 15:
15 = 3 x 5
Hence,
a = 3 x 5 x ....
b = 3 x 5 x ....
lcm (a, b) = 90
prime factorization of 90:
90 = 3 x 5 x 2 x 3
Therefore the possible pairs of a and b are:
Combination 1:
a = 3 x 5 = 15
b = 3 x 5 x 2 x 3 = 90
Combination 2:
a = 3 x 5 x 2 = 30
b = 3 x 5 x 3 = 35
We can conclude the two integers are 15 and 90 or 30 and 45.
Learn more about gcd here:
brainly.com/question/16969353
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Answer:
y = 9 - 5x
[x = -1] 14
[x = 0] 4
[x = 4] -11
Step-by-step explanation:
Step 1: Define
y + 5x = 9
x = -1, 0, 4
Step 2: Solve for <em>y</em>
y = 9 - 5x
Step 3: Plug in values of <em>x</em>
y = 9 - 5(-1) = 14
y = 9 - 5(0) = 4
y = 9 - 5(4) = -11
Answer:
k = -3
Step-by-step explanation:
Given
Variation: Direct
y = -15 when x = 5
Required
Find the constant of variation
A direct variation is represented as:
y = kx
Where
k = constant of variation
Substitute values for x and y
-15 = k * 5
Multiply both sides by ⅕
⅕ * -15 = k * ⅕ * 5
-3 = k * 1
-3 = k
k = -3
Hence, the constant of variation is -3
Answer:
8
Step-by-step explanation:
let the number be n , then
n + 3 = n - 3 ( multiply through by 4 to clear the fraction )
n + 12 = 4n - 12 ( subtract 4n from both sides )
- 3n + 12 = - 12 ( subtract 12 from both sides )
- 3n = - 24 ( divide both sides by - 3 )
n = 8
That is the number is 8