All categories

3 years ago

At noon, ship a is 180 km west of ship

1 answer:

5 0

If we let the coordinates of each ship be (x, y) with the positive directions of these coordinates corresponding to East and North, then the positions of the ships t hours after noon are

Ship A
(-180+35t, 0)

Ship B
(0, 30t)

The distance between them is the "Pythagorean sum" of the difference in their coordinates:
d = √((-180 +35t)² +(-30t)²)
= √(32400 -12600t +2125t²)
The rate of change of this distance is
dd/dt = (2125t -6300)/√(32400 -12600t +2125t²)

At 4 pm, the value of this rate of change is
(2125*4 -6300)/√(32400 -12600*4 +2125*4²)
= 2200/√16000
≈ 17.39 km/h

The distance between the ships is increasing at about 17.39 km/h at 4 pm.

You might be interested in

A basket contains five apples and seven peaches. You randomly select one piece of fruit and eat it. Then you randomly select ano

IgorC [24]

Answer:

Step-by-step explanation:

Total fruits T= 5+7 = 12

No. Of apple n(A) = 5

No. Of peaches n(P) = 7

P(A) 1st = n(A)/T = 5/12

P(P) 2nd = n(p)/(T-1) = 7/11

: P(A and P) = 5/12 × 7/11

= 35/132

4 0

3 years ago

Find the roots of the function f(x) = 3x4 - 48.

Andrew [12]

Answer:

$x=\pm 2\text{ or } x = \pm 2i$

Step-by-step explanation:

We are given:

$0=3x^4-48$

Factor:

$0=3(x^4-16)$

Difference of Two Squares:

$0=3(x^2-4)(x^2+4)$

Zero Product Property:

$(x^2-4)=0\text{ or } x^2+4=0$

Solve:

$x^2=4\text{ or } x^2=-4$

Take the square root. Since we are taking an even-root, it requires plus/minus:

$x=\pm 2\text{ or } x = \pm 2i$

6 0

3 years ago

A=1+Prt solve for p

lilavasa [31]

$A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}$

4 0

4 years ago

Challenge A warehouse store sells 5.5-ounce cans of tuna in packages of 8. A package of 8 cans

Stolb23 [73]

Answer:

Step-by-step explanation:

the warehouse is the best buy because you get 44oz off tuna but if you buy the three pack you get 19.5oz and if you buy the five pack from store you 22.5oz of tuna

so the warehouse has the best deal on tuna

4 0

3 years ago

Do most people your age understand finance?

stealth61 [152]

Answer:

Age 1-NO

Age 2-NO

Age 3-NO

Age 4-NO

Age 5-NO

Age 6-NO

Age 7-NO

Age 8-NO

Age 9-NO

Age 10-NO

Age 11-maybe probably not

Age 12-maybe probably not

Age 13-maybe probably not

Age 14-kinda

Age 15-kinda

Age 16-starting to know more

Age 17-starting to know more

Age 18-pretty sure

Age 19-pretty sure

Age 20-yes

8 0

3 years ago