-2 - 10j = -9j -3<br>Is that <br>no solution<br>one solution<br>infinitely many solution

Is amount off an increase or decrease

Mashutka [201]

Decrease because you taking something off of something

7 0

3 years ago

A 4-pound bag of potatoes costs $3.16 how much would 32 pounds of potatoes costs

zimovet [89]

Answer:

$25.28

Step-by-step explanation:

Since a 4 pound bag cost $3.16 you would do 32 divided by 4 and you would get 8. Then you would do 8 times 3.16 and you get 25.28.

The long way:
4 bags = 3.16
8 bags = 6.32
12 bags = 9.48
16 bags = 12.64
20 bags = 15.80
24 bags = 18.96
28 bags = 22.12
32 bags = 25.28

7 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

A right rectangular prism with square bases has a height of 20 centimeters and a volume of 800 cubic centimeters.

nignag [31]

Answer:

The length of a side of the base is 20 centimeters.

The area of a lateral side between the bases is about 126.5 square centimeters.

Step-by-step explanation:

It's a rectangular prism with a total volume of 800 cu cm, and a height of 20 cm.

So, the base has an area of... 800/20 = 40 sq cm.

The prism is a cube. NO. If it was a cube, the base would be 400 sq cm (20x20), since the height is 20.

The diagonal of the base is 4 centimeters. NO. with a base of 40 sq cm, it's impossible to have a diagonal of 4 cm. A diagonal would form a hypotenuse... and an hypotenuse is longer than the two other sides... an hypotenuse of 4 would mean for example sides of about 2 and 3... which gives 6 sq cm for the base, not 40.

The length of a side of the base is 20 centimeters. COULD BE. The base is 40 sq cm, it could have a side of 20 and the other of 2. Without knowing more about the prism than what's included in the question, we can't say YES and we can't say NO.

The area of a base is 40 square centimeters. Yes

The area of a lateral side between the bases is about 126.5 square centimeters. YES, since the height is 20, that would mean one side of the base would be roughly 6.325 cm... for a base area of 6.325 x 6.325 = 40 sq cm.

7 0

3 years ago

Read 2 more answers

The number is 9,18,27,36,45 what is the question?

MissTica

Hello from MrBillDoesMath!

Answer: I'd guess it's "find the next number in the sequence" (which is 54)

Discussion:

9 * 1 = 9

9 * 2 = 18

9 * 3 = 27

9 * 4 = 36

9 * 5 = 45

9 * 6 = 54

Thank you,

MrB

7 0

3 years ago

Read 2 more answers

-2 - 10j = -9j -3Is that no solutionone solutioninfinitely many solution​

-2 - 10j = -9j -3Is that no solutionone solutioninfinitely many solution