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goldfiish [28.3K]
3 years ago
6

Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (inc

luding the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.
Look at picture.


Approximate how many times greater Saturn's mass is than Mercury's.

A) 200,000
B) 2,000,000
C) 2,000
D) 20,000

Mathematics
1 answer:
makkiz [27]3 years ago
5 0

Answer:

2000 times

Step-by-step explanation:

Given

Sara:

Mercury = 3.302 * 10^{23

Saturn = 5.685 * 10^{26

Sam:

Mercury = 3.302 * 10^{29

Saturn = 5.685 * 10^{32

To determine the number of times, the mass of Saturn is greater than the mass of Mercury, we simply do the following:

Times = \frac{Saturn}{Mercury}

Using Sara's measurement; this gives:

Times = \frac{5.685 * 10^{26}}{3.302 * 10^{23}}

Apply law of indices

Times = \frac{5.685 * 10^{26-23}}{3.302}

Times = \frac{5.685 * 10^3}{3.302}

Times = 5.685/3.302 * 10^3

Times = 1.72 * 10^3

Approximate

Times = 2 * 10^3

Times = 2000

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PLEASE HELP ASAP <br>are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?​
GREYUIT [131]

Answer:

To find the inverse of:

f (x)=\dfrac{4}{x-2}-1

Set the function to y:

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Rearrange to make x the subject:

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\implies (y+1)(x-2)=4

\implies xy-2y+x-2=4

\implies xy+x=2y+6

\implies x(y+1)=2y+6

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Swap x and y:

\implies y=\dfrac{2x+6}{x+1}

Change y to the inverse of the function sign:

\implies f\:^{-1}(x)=\dfrac{2x+6}{x+1}

Rewrite g(x) as a fraction:

g(x)=\dfrac{3}{x+2}-2

\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}

\implies g(x)=\dfrac{3-2(x+2)}{x+2}

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4 0
2 years ago
An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the sam
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Answer:

<h2>1.84feet</h2>

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range R = U\sqrt{\frac{H}{g} }

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}

Squaring both sides we have;

(\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} =  \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet

The arrow will hit the target 1.84feet below the bullseye.

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Read 2 more answers
Tina is saving to buy a notebook computer. She has two options. The first option is to put S200 away initially and save $10 ever
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The equation for the first option is Y=10x + 200
The equation for the second option is Y=30x + 100

X = one month
To find when they would be the same about you have to set the equations equal to each other

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-10x -100 -10x -100

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5 = x

After five months she would save the same amount. To find how much is saved you have to plug in 5 for x in one of the equations. You can always double-check 5 by plugging it in both equations and making sure you get the same answer

Y= 10(5) + 200 = 250

Y= 30(5) + 100 = 250

She would have saved $250 after five months by using either method
6 0
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