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
const2013 [10]
3 years ago
15

A water taxi travels around an island in a path that can be modeled by the equation y =0.5(x - 16). A water skier is skiing alon

g a path that begins at the point
(6,6) and ends at the point (8. - 4).
a. Write a system of equations to model the problem.
b. Is it possible that the water skier could collide with the taxi? Explain
Mathematics
1 answer:
Eddi Din [679]3 years ago
8 0

I realize that the equation is different, but do it in the same way, it'll help! It is given that the water​ taxi's path can be modeled by the equation y =0.5(x - 14)^2. ​Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water​ skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the​ y-intercept of the line.  The​ y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the​ taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of​ equations, solve the system using substitution.​ First, write the equation that models the water​ taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for  y in the equation and then solve for  x. As the expression on the left side of the equation cannot easily be​ factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.

In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.

You might be interested in
Hi pls help this is TIMED
alexandr1967 [171]

What is the question you have?

3 0
3 years ago
Giving brainliest to best answer
Sergio [31]

Answer:

One unit to the right.

Step-by-step explanation:

I entered both equations into desmos and rootx - 1 is one unit to the right.

Desmos is a great tool for graphing

6 0
3 years ago
How do you find the area of a triangle if you only know it's three sides?
DiKsa [7]
You would have to find the height.

To do this, you cut the triangle from the upper vertex to the base to create two new triangles.

Then you use the Law of Cosines. You could use the google calculator for this by searching “law of cosines calculator” and inputting the values, but in case of a test, the formula is a^2 = b^2 + c^2 - 2bc cosA

If you could provide an example of a triangle, I will gladly help you with the steps! Hope this helped!
8 0
3 years ago
Find the value of x.
maxonik [38]

180 = 132 + x + x

180 - 132 = 2x

48 = 2x

x = 24⁰

5 0
3 years ago
Read 2 more answers
How many years will it take for the account to reach $18,600? Round your answer to the nearest hundredth
Margarita [4]
 <span>it depends how the interest is calculated, but there's not much of a difference 

assuming its continuously compouned, you use this formula: A(t)=Pe^(rt), where A is the final amount, P is the initial investment, r is the interest, and t is the time in years 

you want to find t such that A(t)=18,600 so 18,600=1000e^(.0675t) 

you need to use logarithm to figure it out, take the natural log of both sides 

the following properties will come into use: 

ln(a*b)=ln(a)+ln(b) 
ln(a^b)=bln(a) 
ln(e)=1 

taking the natural log 

ln(18,600)=ln(1000e^(.0675t)) 

ln(18,600)=ln(1000)+ln(e^.0675t) 

ln(18600)=ln(1000) + .0675t 

now solve for t: t= (ln(18600)-ln(1000))/.0675 

t=43.31</span>
4 0
3 years ago
Other questions:
  • What is the answer for question 11. Please tell me.
    5·1 answer
  • 5r^2-38r-16 i must factor by grouping but im very lost
    11·1 answer
  • Hasil perhitungan dari akar pangkat dua 9×3+15×5 adalah
    11·1 answer
  • Which expression is equivalent to (7x – 5) – (3x - 2)?
    11·1 answer
  • How to solve x^2+8x+3 using the quadratic formula​
    7·1 answer
  • PLS HELP HELP ME IN math pls:( =/​
    9·1 answer
  • A² + 6 from 7<br> plzz answer i gave u half of my points plz
    14·1 answer
  • If f(x) = -4x^2 - 5x + 2, what is f(3) ?
    9·1 answer
  • If you get paid $15 an hour and you work 50 hours a week how much money do u make in a year
    8·1 answer
  • How are the linear and nonlinear functions the same.​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!