A track is about to past through one way tonel in a form of semi-ellipse  which is 15m across and 4m high if the track has a Wight 14 and high 3m is the track can past yes or no 

To determine if the truck can pass through the tunnel, we need to compare the dimensions of the truck to the shape of the tunnel.

### Tunnel Shape:
The tunnel is in the shape of a semi-ellipse. The standard equation for an ellipse is:

\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]

Where:
- \( a \) is the semi-major axis (half the width of the ellipse),
- \( b \) is the semi-minor axis (half the height of the ellipse).

For this tunnel:
- The width of the tunnel is 15 m, so \( a = 7.5 \) m.
- The height of the tunnel is 4 m, so \( b = 4 \) m.

The equation of the semi-ellipse is then:

\[
\frac{x^2}{7.5^2} + \frac{y^2}{4^2} = 1
\]

### Truck Dimensions:
- The width of the truck is 14 m, so the truck extends 7 m on either side from the center.
- The height of the truck is 3 m.

### Check if the Truck Fits:
We need to check if the truck, which is 7 m wide and 3 m high, fits within the semi-ellipse.

1. The truck extends 7 m from the center horizontally.
2. Using the equation of the ellipse, plug \( x = 7 \) into the equation to find the corresponding height \( y \).

\[
\frac{7^2}{7.5^2} + \frac{y^2}{4^2} = 1
\]

Let me calculate the height \( y \).At a horizontal distance of 7 meters from the center, the height of the semi-ellipse is approximately 1.44 meters. 

Since the truck's height is 3 meters, and the height of the tunnel at that point is only 1.44 meters, the truck will not fit through the tunnel.

The answer is **No**, the truck cannot pass through the tunnel.

Would you like more details or have any questions? Here are some related questions to think about:
1. How does the size of the ellipse impact the design of tunnels?
2. Can the shape of the tunnel be changed to allow larger vehicles?
3. What is the difference between a semi-ellipse and a full ellipse in practical applications?
4. How could we determine if a truck could pass through a rectangular tunnel?
5. What mathematical models help engineers design tunnels?

**Tip**: Always double-check both width and height when determining whether an object can fit through an opening!

A track is about to pass through a one-way tunnel in the form of a semi-ellipse which is 15m across and 4m high. If the track has a width of 14m and height of 3m, can the track pass? Yes or no.

Find out if a truck with a width of 14m and height of 3m can pass through a semi-elliptical tunnel that is 15m wide and 4m high. This problem explores the properties of ellipses and their real-world applications in tunnel design.

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