Mathematics, 16.05.2021 14:00 youngsunc02

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

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Answer from: N72967

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

It is clear that 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

false

step-by-step explanation:

rulers and compasses arent required in order to bisect an angle because when bisecting angles, you're making a "half circle" and considering in order to bisect an angle it wouldn't be straight, you wouldn't need either of the two

Answer from: Quest

step-by-step explanation:

when the line is solid:

it's either < or >

when the line is dashed:

it's either < or >

this > inequality sign means:

greater thanmore thanaboveexceeds

this < inequality sign means:

less thanfewer thanbelow

this > inequality sign means:

greater than/equal tono less thanat leastminimum of

this < inequality sign means:

less than/equal tono more thanat mostmaximum of

about the problem:

since the line is solid, that means it's either < or >

srry i'm not done ! i'll

Which inequality is represented by the graph? which test point holds true for the inequality?

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