Mario’s Water Level Challenge

 

Mario, a tour guide in Palawan, plans to take a tourist to the Undergound River. The tour boat’s speed is affected by the river’s water level, which changes with the tide.

Mario notices the water level (in meters) follows a quadratic equation: h(t) = 2t² + 3t + 1, where t is the time in hours.

At what time (t) will the water level be 7 meters?

• ½ hours

• 3/2 hours

• 5/2 hours

• 7/2 hours

Mario’s Water Level Challenge

Mario, a tour guide in Palawan, plans to take a tourist to the Undergound River. The tour boat’s speed is affected by the river’s water level, which changes with the tide.

Mario notices the water level (in meters) follows a quadratic equation: h(t) = 2t² + 3t + 1, where t is the time in hours.

If the boat's speed is directly proportional to the square root of the water level, and the speed is 10km/h when the water level is 4 meters, what is the speed when the water level is 9 meters?

• 15 km/h

• 18 km/h

• 20 km/hr

• 22 km/h

The Glass Igloo Project

 

In the frozen tundra of Lapland, Finland, stood an architectural wonder: the Glass Igloo. This ethereal structure, composed of glass panels, seemed to defy gravity and blend seamlessly into the snowy landscape. Behind its breathtaking beauty lay a tapestry of intricate mathematical calculations.

The structure's design involves solving various quadratic equations and rational algebraic equations to ensure stability, optimal use of materials, and aesthetic appeal. The height h of the igloo’s main arch is given by the quadratic equation h = − x² + 6x.

What is the quadratic equation given of the Igloo's main arch?

• h = x2 + 6x.

• h = − x2 + 6x.

• h = − x + 6x.

• h = − x + 6.

The Glass Igloo Project

In the frozen tundra of Lapland, Finland, stood an architectural wonder: the Glass Igloo. This ethereal structure, composed of glass panels, seemed to defy gravity and blend seamlessly into the snowy landscape. Behind its breathtaking beauty lay a tapestry of intricate mathematical calculations.

The structure's design involves solving various quadratic equations and rational algebraic equations to ensure stability, optimal use of materials, and aesthetic appeal. The height h of the igloo’s main arch is given by the quadratic equation h = − x² + 6x.

The cost C to produce each glass panel is given by the rational algebraic expression C(x)=100x+2. Calculate the cost when x = 3.

• 15

• 20

• 30

• 50

The Glass Igloo Project

In the frozen tundra of Lapland, Finland, stood an architectural wonder: the Glass Igloo. This ethereal structure, composed of glass panels, seemed to defy gravity and blend seamlessly into the snowy landscape. Behind its breathtaking beauty lay a tapestry of intricate mathematical calculations.

The structure's design involves solving various quadratic equations and rational algebraic equations to ensure stability, optimal use of materials, and aesthetic appeal. The height h of the igloo’s main arch is given by the quadratic equation h = − x² + 6x.

The quadratic equation representing the width w of a glass panel is given by w= x2 - 4x + 4. If the width needs to be at least 2 meters, solve for x.

• x≤1 or x≥3

• x≤0.5 or x≥3.5

• x≤2 or x≥4

• x≤1.5 or x≥2.5

Optimizing Space for Flower Beds and Tents at Balayong Park

Balayong Park is known for its beautiful cherry blossom trees and intricate garden paths. Recently, the park management has decided to add more flower beds in the shape of rectangular plots but with specific constraints on the dimensions.

If a flower bed in Balayong Park has its length represented by x and width by (2x−1)(2x - 1), form the quadratic expression representing the area of the flower bed.

• x(2x+1) = 2x2+x

• x2 + 2x = x3

• x (2x - 1) = 2x2 - x

• x (2x - 1) = 2x2 - 2x - 1

Optimizing Space for Flower Beds and Tents at Balayong Park

Balayong Park is known for its beautiful cherry blossom trees and intricate garden paths. Recently, the park management has decided to add more flower beds in the shape of rectangular plots but with specific constraints on the dimensions.

Given that the area of the flower bed must be less than 30 square meters, form the quadratic inequality and solve for x.

• 2x2 - x < 30; Solve: x < 5 or x > − 6

• 2x2 - x < 30; Solve: x < 3.5 and x > - 4

• 2x2 - x > 30; Solve: x > 5 and x < -6

• 2x2 - x < 30; Solve: x > 3 and x < −5

Grand Palace

 

The Grand Palace is planning to install a series of new arches in its entrance pathway. Each arch's height hh is given by the quadratic expression h=x²+5x+6h. The safety regulations require that the height should be at least 3 meters but not exceed 10 meters.

If the radius r of a circular fountain base at the Grand Palace is given by r= x+2, form the quadratic expression representing the area A of the fountain base.

• A=π(x2+4)

• A=π(x2+4x+4)

• A=π(2x2+2)

• A=π(2x+4)

Grand Palace

 

The Grand Palace is planning to install a series of new arches in its entrance pathway. Each arch's height hh is given by the quadratic expression h=x²+5x+6h. The safety regulations require that the height should be at least 3 meters but not exceed 10 meters.

Given that the area of the fountain base must be less than 50 square meters, form the quadratic inequality and solve for x.

• π(x2+4x+4) <50, Solve: x<3x < 3 or x>−4

• π(x2+4x+4) <50, Solve: x<2.5x < 2.5 and x>−2.5

• π(x2+4x+4) >50, Solve: x>4x > 4 and x<−6

• π(x2+4x+4) <50, Solve: x<1.5x < 1.5 and x>−1

Grand Palace

 

The Grand Palace is planning to install a series of new arches in its entrance pathway. Each arch's height hh is given by the quadratic expression h=x²+5x+6h. The safety regulations require that the height should be at least 3 meters but not exceed 10 meters.

If another fountain base's radius is given by r = 2x + 3, and the area should not exceed 75 square meters, find the range of possible values for x.

• π(2x+3)2≤75; Solve: x≤2 and x≥−3

• π(2x+3)2≤75; Solve: x≤1.5 and x≥−1.5

• π(2x+3)2≤75; Solve: x≤2.5 and x≥−2.5

• π(2x+3)2≤75; Solve: x≤3 and x≥−3