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
Rus_ich [418]
3 years ago
6

1. SPOTLIGHTS Ship A has coordinates (–1, –2) and Ship B has coordinates (–4, 1). Both ships have their spotlights fixated on th

e same lifeboat. The light beam from Ship A travels along the line y = 2x. The light beam from Ship B travels along the line y = x + 5. What are the coordinates of the lifeboat?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
7 0

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

          <u>Position of ship A: ( - 1 , -2 )</u>

          <u>Position of ship B: ( -4 , 1 )</u>

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

         <u>Spotlight Ship A: y = 2x</u>

         <u>Spotlight Ship B: y = x + 5 </u>

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

       

         Spotlight A = Spotlight B

         y = 2x = x + 5

         2x = x + 5

         x = 5 , y = 10

<u>Answer:</u> <em>The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships</em><em>. </em>

       

You might be interested in
Find each square root
weqwewe [10]

Answer:

It actually gave you the answer.

Step-by-step explanation:

If you read closer, it's telling you the answer. It's giving you examples of radicals and such.

6 0
3 years ago
Judah deposited $450 into an account that earns simple interest, and after 4 years, the interest in the account was 90$. What wa
guapka [62]

Answer:

$22.50 I think I'm not 100% sure, Im sorry

Step-by-step explanation:

90/4 is 22.5 a year

4 0
2 years ago
8 3/ 4 as a decimal.
dem82 [27]
Your answer is 8.25 hope this help also remember to hit that brainliest button

4 0
3 years ago
Read 2 more answers
Consider a rabbit population​ P(t) satisfying the logistic equation StartFraction dP Over dt EndFraction equals aP minus bP squa
maria [59]

Solution:

Given :

$\frac{dP}{dt}= aP-bP^2$         .............(1)

where, B = aP = birth rate

            D = $bP^2$  =  death rate

Now initial population at t = 0, we have

$P_0$ = 220 ,  $B_0$ = 9 ,  $D_0$ = 15

Now equation (1) can be written as :

$ \frac{dP}{dt}=P(a-bP)$

$\frac{dP}{dt}=bP(\frac{a}{b}-P)$    .................(2)

Now this equation is similar to the logistic differential equation which is ,

$\frac{dP}{dt}=kP(M-P)$

where M = limiting population / carrying capacity

This gives us M = a/b

Now we can find the value of a and b at t=0 and substitute for M

$a_0=\frac{B_0}{P_0}$    and     $b_0=\frac{D_0}{P_0^2}$

So, $M=\frac{B_0P_0}{D_0}$

          = $\frac{9 \times 220}{15}$

          = 132

Now from equation (2), we get the constants

k = b = $\frac{D_0}{P_0^2} = \frac{15}{220^2}$

        = $\frac{3}{9680}$

The population P(t) from logistic equation is calculated by :

$P(t)= \frac{MP_0}{P_0+(M-P_0)e^{-kMt}}$

$P(t)= \frac{132 \times 220}{220+(132-220)e^{-\frac{3}{9680} \times132t}}$

$P(t)= \frac{29040}{220-88e^{-\frac{396}{9680} t}}$

As per question, P(t) = 110% of M

$\frac{110}{100} \times 132= \frac{29040}{220-88e^{\frac{-396}{9680} t}}$

$ 220-88e^{\frac{-99}{2420} t}=200$

$ e^{\frac{-99}{2420} t}=\frac{5}{22}$

Now taking natural logs on both the sides we get

t = 36.216

Number of months = 36.216

8 0
3 years ago
What’s this answer can someone give me the answer
Vladimir79 [104]

Answer:   slope= -3,5

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • The revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by R(x)=90x-x^2 and the company's t
    13·2 answers
  • I need help in 2 3 4 5 6 7 8
    14·1 answer
  • Drag each equation to show if it could be a correct first step to solving the equation 
    5·1 answer
  • (need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in
    9·2 answers
  • Andre' went to the store where 3 bags of gummie bears were $6.30. How many were 7 bags of gummie bears?
    7·2 answers
  • A percent measures a rate
    14·2 answers
  • Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which is the better buy? Which Item cost less per gol
    10·1 answer
  • Izzy manages the school baseball and softball teams. Part of his job is taking care of equipment and recording statistics about
    11·1 answer
  • Chris rents a car for a total of £375 The rental charges are £150 for the first day and £75 per day after that. For how many day
    5·1 answer
  • Add and simplify the answer 5/8+1/8
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!