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jolli1 [7]
3 years ago
15

Suppose there are 106 (1 million) asteroids that are 0.87 km in radius. If they were all combined into a single sphere, calculat

e the radius of this sphere in km.
Mathematics
1 answer:
Eduardwww [97]3 years ago
8 0

Answer:

87km

Step-by-step explanation:

Volume is proportional to radius cubed, so radius is proportional to the cube root of volume.

Increase volume by a factor of 10^6 and radius increases by a factor of the cube root of 10^6, which is 10^(6/3) = 10^2 = 100.

100 * 0.87 km = 87 km

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If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
\\\\\\
inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
\\\\\\
\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\

\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
5 0
3 years ago
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of the house
Nina [5.8K]

Answer:

(15,18)

Step-by-step explanation:

write two equations with the information provided.

2x + 3y = 84

x + 4y = 87

use the property of substitution to answer.

x + 4y = 87,   x = 87 - 4y

2(87 - 4y) + 3y = 84

174 - 8y + 3y = 84

174 - 84 = 8y - 3y

90 = 5y

90/5 = y

y = 18

Add the value of Y to an original equation. Solve for X

2x + 3(18) = 84

2x + 54 = 84

2x = 84 - 54

2x = 30

x = 30/2

x = 15

8 0
3 years ago
A rectangular prism has a length of 2 y, a width of 3 y, and a height of 5 y. If the volume of the prism is 10,290 units, what i
inessss [21]

Answer:

y=7

Step-by-step explanation:

2x7=14

3x7=21

5x7=35

14x21x35=10,290

6 0
3 years ago
a movie ticket cost $9. a concert ticket cost $45. which equation can be use to find how many times as much the concert ticket c
Maurinko [17]

Answer:

9x5=45

Step-by-step explanation:

4 0
3 years ago
What is the answer to y=1/2x=2=x-1
Alborosie

Answer:

264647401977373+3637397374+739-739376536372801826464783920182773636373+7373839292901-278282

4 0
3 years ago
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