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4 years ago

12

mr, torres took his students to the dolphin show, each row in the stadium had 11 seats, one adult sat at each of a row, and each

group of 4 students was seated between 2 adults , ms, torres sat by himself , how many adults were there

1 answer:

Leto [7]4 years ago

6 0

I think the answer would be ten

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Two planes A and B start from the same place and move in different directions making an angle of 50° between them the speed of p

Alika [10]

Answer:

The distance between them is 230.65 miles

Step-by-step explanation:

Here we use the Cosine formula

$a^2 = b^2 + c^2 - 2bc\ cos\ A\\\\a^2 = 200^2 + 300^2 - 2\times 200\times 300cos50^{\circ}\\\\= 40,000 + 90,000 - 120,000cos50^{\circ}\\\\= 130,000 - 120,000 \times 0.64\\\\= 130,000 - 76,800\\\\a^2= 53,200\\\\a = \sqrt{53,200} \\\\= 230.65\ miles\ per\ hour$

Now the distance for one hour is

= 230.65 ÷ 1

= 230.65 miles

4 0

3 years ago

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

5x+2y=10; (-2, 9) if -2 is x and 9 is y

Dovator [93]

What are you looking for. slope?

4 0

3 years ago

school teacher and needs 22 pieces of wood, 3 over 8 ft long, for a class project. If he has a 9-ft board from which to cut the

tiny-mole [99]

Answer:

Yes, he will have enough 3 over 8 ft pieces for his class.

Step-by-step explanation:

Given:

Number of wood required = 22

Length of each wood, $l=\frac{3}{8}\textrm{ ft}$

Total length of the board, $L=9\textrm{ ft}$

Therefore, the number of woods that can be made using the given board is given as:

$\textrm{Number of woods made}=\frac{\textrm{Total length of board}}{\textrm{Length of each wood}}\\\textrm{Number of woods made}=\frac{L}{l}=\frac{9}{\frac{3}{8}}=9\times \frac{8}{3}=\frac{72}{3}=24$

So, he can make 24 woods of length $\frac{3}{8}\textrm{ ft}$ using the 9 ft board. But he has to make only 22 pieces.

Therefore, he has enough of the wood to make the required number of pieces.

3 0

3 years ago

Jaelyn works 6 hours per day on Thursday, Friday and Saturdays each week. She

VladimirAG [237]

Answer:

1,363.5

Step-by-step explanation:

$15.15 ×6 =90.9(for Thu,Fri,sat)

15.15×24=363.6(for other days)

90.9×3=272.7(total for Thursday, Friday and Saturdays)

363.6× 3( include other days like Monday Tuesday and Wednesday)

1,090.8

therefore total for 6hours days and full days

1,090.8+272.7=1,363.5

7 0

2 years ago