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miv72 [106K]
3 years ago
7

The mass of Saturn is 5.686 × 10^26 tonnes. The mass of Earth is 6.04 × 10²¹ tonnes. How many times heavier is Saturn than Earth

? Give your answer in standard form to a suitable degree of accuracy.
Mathematics
1 answer:
andrey2020 [161]3 years ago
8 0
We simply divide the mass of Saturn with the mass of Earth.
5.686 x 10^26 / 6.04 x 10^21

The rule of significant figures when dividing numbers is that the least amount significant figures must be used in the quotient.

Therefore, Saturn is 9.41 x 10^4 times heavier than Earth.
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Show Work Please Thank You
Misha Larkins [42]

Answer:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

Step-by-step explanation:

We are given the trigonometric equation of:

\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}

Let u = 4x then:

\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Convert u-term back to 4x:

\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Divide both sides by 4:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

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1 year ago
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Given :

A holiday meal cost 12.50 a person plus a delivery fee of $30 at we cater.

The same meal cost $15 a person with no fee at Good Eats.

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Therefore, after 12th order cater will be more value for money.

Hence, this is the required solution.

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