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A farmer plans to build a rectangular pen with one side cut off by a river, as shown below. He has 40 meters of fence to enclose the remaining three sides.

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Write a function to describe the area A enclosed by the fence, in terms of only the width x.

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Hence the ratio of energies is

ES​EV​​=1023(MV​−MS​)​.

Substituting MV​−MS​=9.5−2.3=7.2 gives

ES​EV​​=1010.8=100.8×1010≈6.31×1010.

Therefore about 6.31×1010 Swift Quakes are needed to match the energy of the Valdivia earthquake.

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Tiffany thinks that a penny dropped from the 380 meter tall Empire State Building will accelerate uniformly at gravitational acceleration, 9.8m/s2.

  1. Assuming Tiffany is correct, find how long it takes the penny to fall.

    [3]

Because of drag, the penny does not uniformly accelerate at 9.8m/s2. Instead the acceleration of a penny dropped from the Empire State Building can be modeled by

a(t)=625​e−t/6m/s2.

  1. Determine the highest speed that the penny reaches.

    [3]

Because of her error, Tiffany waits for k seconds longer than she expected for the penny to reach the ground.

  1. Find k.

    [3]
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Perplex helped me realize my potential was much higher than I initially thought. I went from a 5 in DP1 to a 7 in final exams.

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Using Perplex allowed me to improve my math skills through repetition and continuous help from the AI. As a whole it helped me get a strong 6 in final exams.

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Perplex helped me get from a four to a seven in math higher. it has everything you need: tons of problems, animations, and notes on everything. with that and a super helpful support team, they're the best IB math resource I've found.

— Mathieu 🇨🇭

I think this is probably the only site that really contributed to my understanding of many of the more difficult maths topics.

— Amira 🇲🇾

Perplex made everything click - the explanations are intuitive, and the seamless experience lets me move effortlessly between solving problems, learning, and chatting with AI without ever losing momentum.

— Samir 🇦🇪

Perplex helped me realize my potential was much higher than I initially thought. I went from a 5 in DP1 to a 7 in final exams.

— Alex 🇨🇮

Using Perplex allowed me to improve my math skills through repetition and continuous help from the AI. As a whole it helped me get a strong 6 in final exams.

— Arthur 🇫🇷

Perplex helped me get from a four to a seven in math higher. it has everything you need: tons of problems, animations, and notes on everything. with that and a super helpful support team, they're the best IB math resource I've found.

— Mathieu 🇨🇭

I think this is probably the only site that really contributed to my understanding of many of the more difficult maths topics.

— Amira 🇲🇾

Perplex made everything click - the explanations are intuitive, and the seamless experience lets me move effortlessly between solving problems, learning, and chatting with AI without ever losing momentum.

— Samir 🇦🇪

Perplex helped me realize my potential was much higher than I initially thought. I went from a 5 in DP1 to a 7 in final exams.

— Alex 🇨🇮

Using Perplex allowed me to improve my math skills through repetition and continuous help from the AI. As a whole it helped me get a strong 6 in final exams.

— Arthur 🇫🇷

Perplex helped me get from a four to a seven in math higher. it has everything you need: tons of problems, animations, and notes on everything. with that and a super helpful support team, they're the best IB math resource I've found.

— Mathieu 🇨🇭

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