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
Andreas93 [3]
2 years ago
13

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On

Mathematics
1 answer:
uysha [10]2 years ago
6 0

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

h(x)=ax(x-7)             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

4=a(3)((3)-7)

4=a(3)(-4)

\dfrac{4}{(3)(-4)}=a

-\dfrac{1}{3}=a

Putting a=-\dfrac{1}{3}, we get

h(x)=-\dfrac{1}{3}x(x-7)              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)

h(1.5)=-(0.5)(-5.5)

h(1.5)=2.75

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

You might be interested in
Are these(4,1) 1,-3) (2,0) solutions to this graph?
kogti [31]
(4,1) : no because the line is solid.
(1,-3) : yes because the line is not solid.
(2,0) : no because the line is solid.

Solid lines represent < or >, and if a point is on the line directly, it’s not included in the solution set.
7 0
3 years ago
Lana makes $8 an hour plus $12 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week.
Ierofanga [76]

Answer:

A:  W = 8x

B:  12y + 320

C:  44

Step-by-step explanation:

A:  Lana can make $8 an hour.

W = 8x

B:  She makes $12 per hour for every hour of overtime.  This means that she already worked 40 hours with regular pay.  She has already made $320.

40 × $8 = $320

S = 12y + 320

C:  Plug in the amount Lana earned into the second equation.  The second equation will account for pay from both regular and overtime hours.

S = 12y + 320

368 = 12y + 320

368 - 320 = (12y + 320) - 320

48 = 12y

48/12 = (12y)/12

4 = y

y = 4

Lana worked 4 hours of overtime and 40 hours of regular hours.  In total, she worked 44 hours.

4 + 40 = 44

4 0
3 years ago
Read 2 more answers
The student council is planning the school carnival. Each
Assoli18 [71]

Answer: y = 2.50x

Step-by-step explanation:

X represents the number of tickets sold, and because each ticket costs $2.50, the expression would be 2.50x to find how much money is raised, which can be represented as y.

5 0
3 years ago
In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they
vesna_86 [32]

VARIABLE is a symbol which is used for representation in a  math.

According to the statement

we have to explain about the what is a variable.

So, VARIABLE is a symbol which is used for representation in a  math.

It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.

A variable may also be called a data item.

It is used to represent a data like country name, name, age, date of birth etc.

we know that the every thing is changeable. So, like ther things variables are also changeable.

The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.

So, VARIABLE is a symbol which is used for representation in a  math.

Learn more about VARIABLE here brainly.com/question/1295072

#SPJ4

8 0
1 year ago
Find percentage notation for 300/800
astra-53 [7]
37.5 % of 800 is 300 because of division
7 0
3 years ago
Other questions:
  • Two assembly lines I and II have the same rate of defectives in their production of voltage regulators. Six regulators are sampl
    11·1 answer
  • Which is an equivalent ratio to 7:5? 14:12 21:10 21:15
    8·2 answers
  • A group of mountain climbers begin an expedition with 270 pounds of food. They plan to eat a total of 15 pounds per day. Write a
    15·2 answers
  • Triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 t
    15·2 answers
  • on a suspension bridge the roadway is hung from cables hanging between support towers. the cable of one bridge segment of the pa
    8·1 answer
  • Arm span is the physical measurement of the length of an individual's arms from fingertip to fingertip. A man’s arm span is appr
    13·1 answer
  • Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the w
    9·1 answer
  • Find the roots.<br><br> 2x^2 + 4x - 5 =0
    13·1 answer
  • The median of 217, 217, 218, 224.
    8·2 answers
  • How many solutions exist for the system of equations in the graph?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!