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3 years ago

8

A jewerly store received a package of rings that is 16 inches long, 10 inches wide, and 12 inches high. The package contains 1 i

nch cubes that each hold 1 ring. How many rings did the jewerly store receive?

1 answer:

krek1111 [17]3 years ago

6 0

The jewelry store received 38 rings.

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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

Fudgin [204]

Answer:

250 x 3 = 750g

750g is your final answer

7 0

3 years ago

Read 2 more answers

A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times a long as it is wide. Both the banner and

deff fn [24]

Answer:

The answer to your question is

a) Poster width = 3 in

lenght = 9 in

b) banner

width = 2 in

lenght = 10 in

Step-by-step explanation:

a) For the poster

width = x

lenght = 3x

Perimeter of a rectangle = 2base + 2 height

= 2(x) + 2(3x) = 24

2x + 6x = 24

8x = 24

x = 24/8

x = 3

width = 3 in

lenght = 3(3) = 9 in

b) For the banner

width = y

lenght = 5y

Perimeter of a banner = 2 base + 2 height

2 (y) + 2(5y) = 24

2y + 10y = 24

12y = 24

y = 24/12

y = 2

width = 2 in

lenght = 5(2) = 10 in

7 0

3 years ago

Find angle a. <br> You will get 20 points

VARVARA [1.3K]

Answer:

127

Step-by-step explanation:

15+38+a=180

a= 127

6 0

3 years ago

Read 2 more answers

What is 0.194 repeating as a fraction

laiz [17]

Convert to a fraction by placing the decimal number over a power of 10. So the awnser is 97/500
I hope I helped you

4 0

3 years ago