1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Assoli18 [71]
3 years ago
8

At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast i

s the distance between the ships changing at 5 P.M.?
Mathematics
1 answer:
Evgen [1.6K]3 years ago
8 0
<span>The distance between the ships is changing at a rate of 21.393 km/h

</span><span>Step 1: First, you must draw an image to help better understand the problem 
</span>

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as <span><span><span>dA</span><span>dt</span></span>=−35</span> and the rate of Ship B is expressed as <span><span><span>dB</span><span>dt</span></span>=25</span>

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

<span>ShipA:−35<span><span>km</span>h</span>⋅4hr=−140km</span>

Now if we take this <span>−140km</span> and add it to the <span>150km</span> we can see that Ship A is now only <span>10km</span> away from where Ship B began

<span>ShipB:25<span><span>km</span>h</span>⋅4hr=100km</span>

This means that Ship B is now <span>100km</span> from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→<span>102</span>+<span>1002</span>=<span>z2</span></span>

<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span></span>

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

<span><span>x2</span>+<span>y2</span>=<span>z2</span>→2x<span><span>dx</span><span>dt</span></span>+2y<span><span>dy</span><span>dt</span></span>=2z<span><span>dz</span><span>dt</span></span></span>

We can simplify by canceling out the 2's

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

Step 5: Write down all the information and then plug into equation

<span>x=10and<span><span>dx</span><span>dt</span></span>=−35</span>
<span>y=100and<span><span>dy</span><span>dt</span></span>=25</span>
<span>z=<span>√<span><span>102</span>+<span>1002</span></span></span>and<span><span>dz</span><span>dt</span></span>=?</span>

Now plug in the information

<span>x<span><span>dx</span><span>dt</span></span>+y<span><span>dy</span><span>dt</span></span>=z<span><span>dz</span><span>dt</span></span></span>

<span>10<span>(−35)</span>+100<span>(25)</span>=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>−350+2500=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>2150=<span>√<span><span>102</span>+<span>1002</span></span></span><span><span>dz</span><span>dt</span></span></span>

<span>21.393=<span><span>dz</span><span>dt</span></span></span>

The distance between the ships are increasing at a rate of 21.393 km/h

You might be interested in
What is the common ratio of 2, 10/3, 50/9
mojhsa [17]

The common ratio of 2, 10/3, 50/9 is \frac{10}{6}

<u>Solution:</u>

Given, series of elements are 2, \frac{10}{3}, \frac{50}{9}

We have to find the common ratio of the above given series.

We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.

So, now take \frac{10}{3} and 2

\text { Then, common ratio }=\frac{\frac{10}{3}}{2}

\begin{array}{l}{\text { Common ratio }=\frac{10}{3} \times \frac{1}{2}} \\\\ {\text { Common ratio }=\frac{10}{3 \times 2}=\frac{10}{6}}\end{array}

Hence, the common ratio of the given series is \frac{10}{6}

6 0
3 years ago
Please solve (-3×+15)+(-3×+2)
koban [17]
(-3x + 15) + (-3x + 2)
Simplify by combining like terms.
-6x + 17

-6x + 17
3 0
3 years ago
Read 2 more answers
Talia gave her hairdresser a 20 percent tip, which amounted to $7. What was the price of the service before the tip?
mina [271]
I don't know if I did it right but here's my guess. I think you multiply 7 by 20% and that gives you 1.40 as a result. Compared to the other method I used (division), I'm pretty sure I'm right since the other result was 35. Doesn't make sense if the end amount was $7.
4 0
3 years ago
Read 2 more answers
If f(x) = g(x+1) and g(x) = x^2, find the value of f(3).
Elena-2011 [213]

\bf \begin{cases} f(x)=&g(x+1)\\ f(3)=&g(3+1)\\ &g(4)\\[-0.5em] \hrulefill& \hrulefill\\ g(x)=&x^2\\ g(4)=&4^2\\ &16 \end{cases}\qquad \qquad f(3)\implies g(4)\implies 16

8 0
3 years ago
Which step is included in the graph of the function f(x)=[x-1]? (the brackets are ceiling functions symbols)
KiRa [710]

we are given

f(x)=[x=1]

where bracket means ceiling functions

we know that

Ceiling  function returns the least value of the integer that is greater than or equal to the specified number

so, we can check each options

option-A:

-4\leq x

At x=-4:

f(x)=[-4-1] =-5

For x<-3:

Let's assume

x=-3.1

f(x)=[-3.1-1] =[-4.1]=-5

so, this interval is TRUE

option-B:

-2\leq x

At x=-2:

f(x)=[-2-1] =-3

For x<-1:

Let's assume

x=-1.1

f(x)=[-1.1-1] =[-2.1]=-3

so, this is FALSE

7 0
3 years ago
Read 2 more answers
Other questions:
  • 2 Points
    10·1 answer
  • Is this correct? Yes or nah
    7·1 answer
  • Put these questions in order from least to greatest 3/8 19/24 2/3
    9·1 answer
  • What is the distance between the points (2, 5) and (5, 7)?
    15·2 answers
  • When u flip a fair coin what is the probablity the outcome would be tales round your answer to 2 decimal place s?
    15·1 answer
  • Write the slope-intercept form of the equation that passes through the point (-2, 3) and is parallel to the line y = -6x - 9 y =
    11·1 answer
  • A hotel had a number of meeting rooms, m, available for events. Each meeting room has 325 chairs.
    11·2 answers
  • Sole the following problems by setting up a proportion, then solving by cross multiplying. if possible, set up the proportion as
    11·1 answer
  • Can you pls help me with my homework I need help
    14·1 answer
  • Chuy wants to buy a new television. The television costs $1,350. Chuy decides to save the same amount of money each week, for 27
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!