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 yogurt costs 45p. How many yogurts can be bought for five pounds?
Iteru [2.4K]
1 yogurt = 45p
1p = ? yogurt 

1 ÷ 45 = 0.02

5 × 0.02 = 0.10

0.10 yogurt can be bought with 5p (pounds)
8 0
2 years ago
Decide which of the two points on the graph of the line<br> X=0<br> A. 0,7<br> B. -4,0
MrMuchimi
When x = 0

A. 0, 7 is your answer

hope this helps
4 0
3 years ago
A researcher is interested in estimating the mean weight of a semi trailer truck to determine the potential load capacity. She t
Kaylis [27]

Answer: 95% confidence interval = 20,000 ± 2.12\times\frac{1500}{\sqrt{17} }

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

Step-by-step explanation:

Given :

Sample size(n) = 17

Sample mean = 20000

Sample standard deviation = 1,500

5% confidence

∴ \frac{\alpha}{2} = 0.025

Degree of freedom (d_{f}) = n-1 = 16

∵ Critical value at ( 0.025 , 16 ) = 2.12

∴ 95% confidence interval = mean ± Z_{c}\times\frac{\sigma}{\sqrt{n} }

Critical value  at 95% confidence interval = 20,000 ± 2.12\times\frac{1500}{\sqrt{17} }

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

3 0
3 years ago
Sara rolls a fair dice 600 times.<br> How many times would Sara expect to roll a six?
masya89 [10]

Answer:

100

Step-by-step explanation:

possibility of getting 6 in one roll = 1/6

Possibility of getting 6 in 600 rolls = 1/ 6 x 600 = 100

I hope im right!!!

6 0
3 years ago
How do I show work for this question?, A train travels at an average speed of 67.5 miles per hour. At this speed how far could t
KatRina [158]

Answer: 219.375 miles

<u>Step-by-step explanation:</u>

d = r * t

   = 67.5 * 3.25

   = 219.375

5 0
3 years ago
Other questions:
  • Round off 0.043 to one significant figure
    13·1 answer
  • I need help and i need it fast!
    5·1 answer
  • 1 + 1 is 2 2 plus 2 is 4 4+4 is 8+ 8 it is​
    12·2 answers
  • What is the answer (10 subtract 2)2+(5+16 subtract 2)
    5·1 answer
  • Simplify (x+3)(x-1) - x(x+2)
    12·2 answers
  • Xavier performs the elementary row operation represented by Ri - R, on matrix A.​
    7·1 answer
  • A restaurant was making their own version of Arnold Palmer (lemonade and iced tea). The ratio of lemonade to iced tea is 4:5. Wh
    8·2 answers
  • Find the mean and median of the set of numbers: <br> 5,9,3,5,3,5?
    14·1 answer
  • Teresa is a software engineer. Her base salary is $2400 and she makes $80 more for every copy of “Math is Fun”. Her total pay ,
    14·1 answer
  • What is the exact value of x
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!