Mathematics, 16.05.2021 14:00 Faithmel

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On the ceiling 3 m from each end of the base there are light fixtures. The height to light
fixtures is 4 m. A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive
through the tunnel? Is this possible? (Give full algebraic solution.

Answers: 3

Show answers

Answers

Answer from: Quanashiar

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.

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

the ceiling 3 m

Answer from: Quest

the answer is a

step-by-step explanation:

39.00 x 24 = total installment price

carrying installment price - cash price

needed to save the .00/

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Look at the following graph of the given equation. determine whether the equation is a function. explain why or why not.

Answers: 1

Answer

Mathematics, 21.06.2019 17:00

Simply 8x squared + 5(7x squared- x) - 2x =

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

George has seven boxes of five pencils. giulio three boxes of eight pencils. one of the boys arranges all his pencils equally into two groups. was this george or giulio how many are in each group explain

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Answer asap evaluate 4-0.25g+0.5h4−0.25g+0.5h when g=10g=10 and h=5h=5.

Answers: 3

Answer

You know the right answer?

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On the ceiling 3 m...

Questions

Mathematics, 20.11.2020 19:50

There are 5 girls and 1 boy taking swimming lessons. The ratio that compares the number of girls taking swimming lessons to the total number of stude...