Use the drawing tool(s) to form the correct answer on the provided number line.

lawyer [7]

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.

5 0

2 years ago

Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train. Mason leaves the train station in Portland and dr

s2008m [1.1K]

Answer:Lilah's speed on the train is 60 mph and Mason's speed is 75 mph

Step-by-step explanation:

Let x represent the speed of Lilah.

Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train.

Distance = speed × time

Distance covered by Lilah in moving from Portland to Seattle would be

3 × x = 3x

It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train.

It means that Mason's speed is

x + 15

Distance covered by Mason would be

2.4(x + 15) = 2.4x + 36

Since the distance from Portland to Seattle is the same, then

3x = 2.4x + 36

3x - 2.4x = 36

0.6x = 36 x = 36/0.6 = 60 mph

Mason's speed would be 60 + 15 = 75 mph

7 0

2 years ago

What are the steps in solving this problem?

asambeis [7]

What I see is that they are multiplying by 5 so the last one is 10 x 5 which equals 50!

5 0

2 years ago

Read 2 more answers

£980 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as

Nitella [24]

Sarah has received £ 294

Solution:

Given that £980 is divided between Caroline, Sarah & Gavyn

Let "c" be the amount received by caroline

Let "s" be the amount received by sarah

Let "g" be the amount received by gavyn

Caroline gets twice as much as Sarah

amount received by caroline = twice as much as Sarah

amount received by caroline = 2(amount received by sarah)

c = 2s ---- eqn 1

Sarah gets three times as much as Gavyn

amount received by sarah = three times as much as Gavyn

amount received by sarah = 3(amount received by gavyn)

s = 3g ------- eqn 2

Given that total amount is 980

c + s + g = 980 --- eqn 3

Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"

From eqn 2,

$g = \frac{s}{3}$ --- eqn 4

Substitute eqn 1 and eqn 4 in eqn 3

$2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294$

Thus sarah has received £ 294

7 0

3 years ago

C and D are mutually exclusive events. Find P(C or D). P(C)= 3/7= P(D)= 4/7 P(C or D)

IgorLugansk [536]

Answer:

$P(C\ or\ D) = 1$

Step-by-step explanation:

Given

$P(C) = \frac{3}{7}$

$P(D) = \frac{4}{7}$

Required

$P(C\ or\ D)$

Since the events are mutually exclusive, then:

$P(C\ or\ D) = P(C) + P(D)$

So, we have:

$P(C\ or\ D) = \frac{3}{7} + \frac{4}{7}$

Take LCM

$P(C\ or\ D) = \frac{3+4}{7}$

$P(C\ or\ D) = \frac{7}{7}$

$P(C\ or\ D) = 1$

3 0

2 years ago