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Nostrana [21]
2 years ago
7

There is still controversy about whether or not Pluto should be considered a planet. Although planets are mainly defined by thei

r orbital path (the condition that prevented Pluto from remaining a planet), the issue of size is something to consider. The table below lists the planets, including Pluto, and their approximate diameters in meters.
Planet Approximate Diameter (m)

Mercury 4.88 × 10^6

Venus 1.21 × 10^7

Earth 1.28 × 10^7

Mars 6.79 × 10^6

Jupiter 1.43 × 10^8

Saturn 1.2 × 10^8

Uranus 5.12 × 10^7

Neptune 4.96 × 10^7

Pluto 2.3 × 10^6


a. Name the planets (including Pluto) in order from smallest to largest.


b. Comparing only diameters, about how many times larger is Jupiter than Pluto?
Mathematics
1 answer:
andrezito [222]2 years ago
6 0

9514 1404 393

Answer:

  a) Pluto, Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter

  b) 62

Step-by-step explanation:

When all the numbers are in scientific notation, as these are, the numbers with the smallest exponent are smaller. If numbers have the same exponent, the number with the smaller mantissa is smaller.

a) least-to-greatest diameter, the order is ...

  Pluto, Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter

__

b) The ratio of diameters of Jupiter and Pluto is ...

  (1.43×10^8)/(2.3×10^6) = 6.2×10^1 = 62

Jupiter's diameter is about 62 times that of Pluto.

_____

<em>Additional comment</em>

Your calculator or spreadsheet can work directly with numbers in scientific notation.

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A farmer sells 8.9 kilograms of pears and apples at the farmer's market.
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Answer:

2.225 kg

Step-by-step explanation:

We know that the total weight the farmer sold was 8.9 kilograms.

- 3/4 of this weight is apples, and the rest is pears.

Therefore, to calculate the amount of kilograms of pears   she sold at the farmer's market (which you can call x), you need to apply the following procedure.

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Look at this graph.
Shtirlitz [24]

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It's exponential

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3 years ago
Solve for r in the formula S = L - rL.
strojnjashka [21]
Subtract L from both sides
S - L = L - L -rL
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4 0
3 years ago
Read 2 more answers
Please help. Thanks &lt;3
4vir4ik [10]
The answer would be A.
Deena is correct because that is not a rational number
Irrational numbers are numbers that are crazy and don’t have an end to them. Example would be pi because it goes on forever and ever. But it you have something that is straight to the point like 2.3 or -4/7 these are RATIONAL because they have an end and are “contained”, this goes for numbers that are repeating too.. if you have like 2.3repeating, then this is also rational because you know what the number is, and it is consistent.
I hope this helps explain rational and irrational a little better :)
6 0
3 years ago
Read 2 more answers
If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand.
densk [106]

Answer:

The demand reduces by $7.12 per month

<em></em>

Step-by-step explanation:

Given

p\to price

x \to demand

2x^2+5xp+50p^2=24800.

p =10; \frac{dp}{dt} = 2

Required

Determine the rate of change of demand

We have:

2x^2+5xp+50p^2=24800.

Differentiate with respect to time

4x\frac{dx}{dt} + 5x\frac{dp}{dt} + 5p\frac{dx}{dt} + 100p\frac{dp}{dt} = 0

Collect like terms

4x\frac{dx}{dt} + 5p\frac{dx}{dt} = -5x\frac{dp}{dt}  - 100p\frac{dp}{dt}

Factorize

\frac{dx}{dt}(4x + 5p) = -5(x  + 20p)\frac{dp}{dt}

Solve for dx/dt

\frac{dx}{dt} = -\frac{5(x  + 20p)}{4x + 5p}\cdot \frac{dp}{dt}

Given that: 2x^2+5xp+50p^2=24800. and p = 10

Solve for x

2x^2 + 5x * 10 + 50 * 10^2 = 24800

2x^2 + 50x + 5000 = 24800

Equate to 0

2x^2 + 50x + 5000 - 24800 =0

2x^2 + 50x -19800 =0

Using a quadratic calculator, we have:

x \approx -113\ and\ x\approx88

Demand must be greater than 0;

So: x=88

So, we have: x=88; p =10; \frac{dp}{dt} = 2

The rate of change of demand is:

\frac{dx}{dt} = -\frac{5(88  + 20*10)}{4*88 + 5*10} * 2

\frac{dx}{dt} = -\frac{5(288)}{402} * 2

\frac{dx}{dt} = -\frac{2880}{402}

\frac{dx}{dt} \approx -7.16

<em>This implies that the demand reduces by $7.12 per month</em>

8 0
3 years ago
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