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
Vinvika [58]
3 years ago
10

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

nd (7, –13), and the center of the arch on the bridge is located at (0, 0). Find the equation of the arch of the bridge.
Mathematics
1 answer:
sdas [7]3 years ago
5 0

Answer:

y=-\dfrac{13}{49}x^2

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

y=ax^2+bx+c

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

-13=a(-7)^2+b(-7)+c

49a-7b+c=-13

(x,y) = (7,-13)

-13=a(7)^2+b(7)+c

49a+7b+c=-13

(x,y) = (0,0)

0=a(0)^2+b(7)+c

c=0

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13

49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13

we can solve these two equation using the elimination method, by simply adding the two equations

\quad\quad49a-7b=-13\\+\quad49a+7b=-13

------------------------------

\quad\quad 98a=-26

\quad\quad a=-\dfrac{13}{49}

Now we can plug this value of a in any of the two equations.

49a-7b=-13

49\left(-\dfrac{13}{49}\right)-7b=-13

-13-7b=-13

-7b=0

b=0

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

y=\left(-\dfrac{13}{49}\right)x^2+0x+0

y=-\dfrac{13}{49}x^2

49y=-13x^2

This our equation of the arch!

You might be interested in
Least to greatest 0.45, -0.48, 8/25
mr_godi [17]

Answer:

-0.48, 8/25, 0.45

Step-by-step explanation:

(plz brainliest if u can)

3 0
3 years ago
Read 2 more answers
Find the slope of the line
dmitriy555 [2]
-5/5 do rise over run
4 0
2 years ago
Multiply.<br><br> 2.5(-4) <br><br><br><br><br><br> eeeeeeeeeeeeeeeeeeeeeeee
lidiya [134]

Answer:

x = 5/8 = 0.625

Step-by-step explanation:

8 0
3 years ago
Which algebraic expression models the sum of 3 coins and c coins?
SpyIntel [72]
3+c i think that the answer.
7 0
3 years ago
3( 2x - 9) + 15 = 60
GarryVolchara [31]

Answer:One solution was found : x = 12. Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the ...

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Twenty times the square of a non zero number is equal to 20 times the number.
    13·2 answers
  • What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 t imes the l
    14·2 answers
  • your family goes to a southern -style restaurant for dinner. there are 6 people in your family .some order the chicken dinner fo
    5·1 answer
  • Need help solving this
    10·1 answer
  • What is (x+3)+(2xx+-5
    6·1 answer
  • 12 more than the quotient of a number and eight
    14·2 answers
  • 6. Joseph has $60 in a savings account. Each week he deposits $12 into the account. Which expression is equivalent to the total
    7·1 answer
  • HELPP i'll give brainliest for the CORRECT answer
    9·2 answers
  • If 4/3 liters of water are enough to water 2/5 of the plants in the house, how som:
    6·2 answers
  • This ven diagram shows sports played by 10 students.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!