Explanation: Resonance occurs when an external force, such as sound waves or physical vibrations, matches an object's natural frequency. When this alignment happens, the object vibrates with increased intensity, potentially leading to structural failure. In this case, the vibrations caused by the sound could be strong enough to impact the stability of the popsicle sticks bridge.

To further investigate, he constructs the bridge again and plays a buzzer using a controller that emits various frequencies corresponding to music notes in a random sequence. He discovers that the bridge collapses after the 6th second when he plays the notes in the sequence Re, Mi, Fa, So, Ti, La, Do, with each tone playing for one second. 

The approx frequencies for each note are as follows:

Do: 250 Hz | Re: 300 Hz | Mi: 350 Hz | Fa: 400 Hz | So: 450 Hz | La: 500 Hz | Ti: 550 Hz

Question: Identify the frequency notes that, when played for 20 milliseconds, will cause the bridge to collapse.

Hint: Hertz (Hz) measures how many cycles happen per second, so 1 Hz equals 1 wave per second.

Eager to explore further, Evan built bridges using toothpicks, pencil leads, pins, and more popsicle sticks. To further investigate, he constructs the bridge again and plays a buzzer using a controller to produce the music notes “Do Re Mi Fa So La Ti,” each for one second. To his surprise, the pencil lead bridge fell in the 2nd second, the popsicle sticks bridge in the 4th second, the pin bridge in the 5th second, and the toothpick bridge in the 7th second.

Question: Identify the wave pattern that will keep the bridges intact (without collapsing) when the notes are played in the given sequence for 5 seconds

Hint: Hertz (Hz) measures how many cycles happen per second, so 1 Hz equals 1 wave per second.

The optimal levels of nutrients for healthy crop growth are shown in the table.

Nutrient levels are acceptable if they vary by up to 15% above or below the optimal values.

The sensor readings for each section are shown in the table.

Plants will show specific leaf colour changes if any of the nutrient levels fall outside the acceptable range. The farmer notices abnormal leaf colours and must figure out which sections are at the highest risk based on both deficiency and excess of nutrients.

Nutrient Imbalance Effects:

Nitrogen Deficiency: Yellowing of leaves

Nitrogen Abundance: Dark green leaves

Phosphorus Deficiency: Purple patches on leaves

Phosphorus Abundance: Dark red leaves

Potassium Deficiency: Browning and curling of leaf edges

Potassium Abundance: Scorched leaf edges and leaf drop

Problem: Given the nutrient imbalances and the effects of both deficiency and abundance on leaf colour, what leaf colour changes can be expected in each section?

The optimal levels of nutrients for healthy crop growth are shown in the table.

The sensor readings for each section are shown in the table.

Nutrient levels are acceptable if they vary by up to 10% above or below the optimal values.

Plants will show specific leaf colour changes if any of the nutrients fall below the acceptable range, nutrient deficiencies.

Stages of Deficiency:

Nitrogen (N): Yellowing of lower leaves

Phosphorus (P): Purple patches on leaves

Potassium (K): Brown edges and curling

Problem: Given the nutrient imbalances and the effects of deficiency on leaf colour, what leaf colour changes can be expected in each section?