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luda_lava [24]
3 years ago
5

Need help solving this question please.

Mathematics
1 answer:
jok3333 [9.3K]3 years ago
4 0

Answer: b) they loaded 112356 lbs of cargo

Step-by-step explanation:

When a boat or an object floats in water, the volume of water that it displaces is equivalent to its weight.

When moving into the port, the cargo boat displaced 2200 ft³ of water. Since the density of water is 62.42 lb/ft³ and mass = density × volume, then the mass of the cargo boat on entering the port is

2200 × 62.42 = 137324 lbs

On leaving the port, it displaces 4000 ft³ of water. The mass of the cargo boat on leaving the port is

4000 × 62.42 = 249680 lbs

The difference in both masses is

249680 - 137324 = 112356 lbs

Therefore, they loaded 112356 lbs of cargo

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I need to solve the equation please help me
lesantik [10]

Answer:

\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

Step-by-step explanation:

We are given the equation:

4\sin^2(x)+6\sin(x)+2=0

First, we can divide everything by 2:

2\sin^2(x)+3\sin(x)+1=0

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

2u^2+3u+1=0

Solve for u. Factor:

(2u+1)(u+1)=0

Zero Product Property:

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Solving for both cases:

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And by substitution:

\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

\displaystyle x=\frac{3\pi}{2}+2n\pi

All together, our solutions are:

\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}

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3 years ago
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Step-by-step explanation:

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