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igor_vitrenko [27]
3 years ago
6

Driving me nuts this one.

Mathematics
1 answer:
gulaghasi [49]3 years ago
4 0
Hmmm let hmm come to think..5£ is a bit too much for some junk glass anyway =) hehee, anyhow. so 5cents then

let us nevermind the price for now, and see how many grams are needed for the 6hours

so 1 bottle (500 grams), gives Adam 7.5 minutes of oven time
how many grams will it be for 6hrs or 6 * 60 = 360 minutes?

\bf \begin{array}{ccllll}
grams&minutes\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
500&7.5\\
x&360
\end{array}\implies \cfrac{500}{x}=\cfrac{7.5}{360}
\\\\\\
\textit{that'll give you, }\boxed{?}\textit{ grams of glass for 6hrs}\\\\
\textit{divide by 1000 to make it Kgs}\implies \cfrac{\boxed{?}}{1000}Kgs
\\\\\\
\textit{is 5cents per Kgs of glass, so }\cfrac{\boxed{?}}{1000}\cdot 5

that's how many "p" (pennies? pence? pounds?) will it be for 6hrs of oven time for Adam
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Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut
frozen [14]

Answer:

a)\sqrt{144-288t+208t^2} b.) -12knots, 8 knots c) No e)4\sqrt{13}

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved 12\dot t (n.m) and ship B has moved 8\dot t (n.m). We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}

b)

We want to find \frac{ds}{dt} for t=0 and t=1

\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0

Since function f(x)=199-288x+208x^2 is quadratic, concave up and has no real roots, we know that 199-288x+208x^2>0 for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

                                                \lim_{t \to \infty} \frac{ds}{dt}

So, lets check this limit:

\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}

Notice that:

4\sqrt{13}=\sqrt{12^2+5^2}=√(speed of ship A² + speed of ship B²)

5 0
3 years ago
Circle has rad of 1.5m what angle subtended at center of circle by arc of 1m
Mumz [18]
120 degrees or 0.67 radians
5 0
3 years ago
The table shows the cost of renting movies online. Number of Movies Cost 1 $3.99 2 $7.98 3 $11.97 4 $15.96 5 $19.95 What does th
Iteru [2.4K]

Answer: A


Step-by-step explanation: If you subtract each price by the price lower then it. Ex: $19.95 - $15.96 = $3.99, $15.96 - $11.97 = $3.99 and so on. They all equal $3.99.


3 0
3 years ago
How would I answer this question? Can someone please help me, and explain why. Thank you.
Serjik [45]
Can you tell me what you need help because it doesn't says
4 0
3 years ago
Please help I am struggling really bad thank you so much
Pavlova-9 [17]

Answer:

1) A

2) A

3) C

Step-by-step explanation:

7 0
2 years ago
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