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murzikaleks [220]
3 years ago
6

A cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,46

2. Model the numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality.
x ≤ 2,052 and x ≥ 2,462
x ≥ 2,052 and x ≤ 2,462
x ≤ 2,052 and x ≤ 2,462
x ≥ 2,052 and x ≥ 2,462
Mathematics
2 answers:
GaryK [48]3 years ago
8 0

Answer:

B

Step-by-step explanation:

At least means that the amount is at least be this much, but it could be more:greater than or equal to. Since the ship could only take a certain amount of passengers , the amount of passengers should be less than the limit or equal to the limit, but can't be over.

If you still don't understand, tell me the part you don't understand.

Nana76 [90]3 years ago
7 0

Answer: x\geq2,052\text{ and }x\leq2,462

Step-by-step explanation:

Given : A cruise ship needs to book at least (more than or equals to) 2,052 passengers to be profitable, but the most (less than or equals to) passengers the ship can accommodate is 2,462.

Let x denotes the accommodate is 2,462. Model the numbers of passengers that need to be booked to ensure the cruise line makes a profit.

Then , we have the following compound inequality :-

x\geq2,052\text{ and }x\leq2,462

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A family of 7 are seated in their circular dining table . In how many ways can they be arranged?​
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Step-by-step explanation:

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Gre4nikov [31]

Answer:

A.  77.4

Step-by-step explanation:

<u>Linear approximation formula</u>

L(x)=f(a)+f'(a)(x-a)

Given function:

f(x)=(x+1)^2

\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If  $y=f(u)$  and  $u=g(x)$  then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times \dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}

\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If  $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}

\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If  $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}

Use the chain rule to differentiate the function.

\textsf{Let }\:y=u^2\:\textsf{ where }u=(x+1)

Differentiate the two parts separately:

  y=u^2 \implies \dfrac{\text{d}y}{\text{d}u}=2u

  u=x+1 \implies \dfrac{\text{d}u}{\text{d}x}=1

Put everything back into the chain rule formula:

\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =2u \times 1\\ & = 2u \\ & = 2(x+1)\\ & = 2x+2 \end{aligned}

\textsf{Therefore, }\:f'(x)=2x+2..

The <u>linear approximation</u> at a = 8 is:

\begin{aligned}L(x) & =f(a)+f'(a)(x-a)\\\\\implies L(x) & = f(8)+f'(8)(x-8)\\& = (8+1)^2+(2(8)+2)(x-8)\\& = 81+18(x-8)\\& = 18x-63\end{aligned}

Finally, substitute x = 7.8 into the <u>linear approximation equation</u>:

\begin{aligned}\implies L(7.8) & =18(7.8)-63\\& = 140.4-63\\& = 77.4\end{aligned}

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