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
Igoryamba
2 years ago
14

The arch beneath a bridge is​ semi-elliptical, a​ one-way roadway passes under the arch. The width of the roadway is 38 feet and

the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

Mathematics
1 answer:
forsale [732]2 years ago
5 0

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

\frac{x^2}{a^2}+\frac{y^2}{b^2}

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

a=\frac{38}{2}=19ft

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}

and we can simplify the equation, so we get:

\frac{x^2}{361}+\frac{y^2}{144}

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

\frac{y^{2}}{144}=1-\frac{x^{2}}{361}

y^{2}=144(1-\frac{x^{2}}{361})

we can add everything inside parenthesis so we get:

y^{2}=144(\frac{361-x^{2}}{361})

and take the square root on both sides, so we get:

y=\sqrt{144(\frac{361-x^{2}}{361})}

and we can simplify this so we get:

y=\frac{12}{19}\sqrt{361-x^{2}}

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

y=\frac{12}{19}\sqrt{361-(8)^{2}}

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

You might be interested in
a restaurant has an all-you-can-eat buffet. They charge $13.95 per person. what is the constant of proportionality?​
Evgen [1.6K]

Answer:

staurant has an all-you-can-eat buffet. They charge $13.95 per person. what is the constant of proportionality?​

Step-by-step explanation:

3 0
3 years ago
Involves 6 suspects, 6 weapons and 9 rooms. one of each is randomly chosen and the object of the game is to guess the chosen thr
Tcecarenko [31]
Their would be 21 different solutions for this problem
7 0
3 years ago
PLEASE HELP ASAP NO LINKS
insens350 [35]

<u><em>function </em></u>: p(x) = 65 + 25(x)

for 3 sells

  • p(3) = 65 + 25(3)
  • p(3) = 140

for 10 sells

  • p(10) = 65 + 25(10)
  • p(10) = 315

So,

140 ≤ p(x) ≤ 315

8 0
2 years ago
Read 2 more answers
Caroline walks 1/2 inches second?
defon

Answer: half a inch is 1.27 centimeters

Step-by-step explanation:

4 0
3 years ago
NEED AN ANSWER QUICKK Ayo and Ria are both travelling by train.
Serhud [2]

Answer:

28

Step-by-step explanation:

I guessed it right on hegarty maths and this was the answer

5 0
2 years ago
Other questions:
  • If f(x)=-x+3 find f(-3)
    7·2 answers
  • A circular plate has a radius of 13 centimeters.
    11·2 answers
  • ASAP What statements are true regarding the given statement and diagram?
    5·2 answers
  • At a bargain store. Tanya bought 5 items that each cost the same amount. Tony bought 6 items that each cost the same amount, but
    5·2 answers
  • How does a Nine and thirty six hundredths with a decimal point
    12·2 answers
  • Kevin is planting a triangular garden where 2 sides of the garden come together at an angle of 35°. If 1 unknown angle in the tr
    6·1 answer
  • Sara has $175 and wants to start saving more money so she opens a savings account and deposits the $175 in it to start. The func
    9·1 answer
  • Two pairs of jeans cost $75 before tax. If the total tax paid for the two pairs of jeans was $6, what is the percentage of tax?
    5·1 answer
  • Solve by using elimination. Express your answer as an Ordered pair (-x +2y=3 3x-2y=7
    5·1 answer
  • If you were to use the substitution method to solve the following system, choose the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!