metadata
library_name: transformers
license: apache-2.0
language:
- en
widget:
- example_title: Reasoning
text: >
<|im_start|>system
You are Hyperion, an AI assistant developed by Sebastian Gabarain with a
focus in reasoning, coding, science, and other general-purpose subjects.
You are an AI assistant that follows instruction extremely well. Help as
much as you can.
<|im_end|>
<|im_start|>user
In this task, you are given a description of an object and its
surroundings. Your
task is to describe the motion of the object mentioned in the description
using
differential equations. The answer should be a mathematical expression in
t. Description:
A ball is thrown up at 30 ft/sec from 3 feet off the ground. Solve this
step-by-step,
explaining each step in detail.
<|im_end|>
<|im_start|>assistant
output:
text: >
Hyperion here. The task requires you to describe the motion of a ball
thrown up using differential equations. Here's the detailed explanation
of how to solve it:
1. Identify the given information:
- Initial velocity (v0): 30 ft/sec
- Initial height (y0): 3 feet off the ground
2. Determine the acceleration due to gravity (g) at sea level, which is
approximately -32.2 ft/s^2. Since we're dealing with a short distance
and not very high altitudes, we can consider this value of g as
constant.
3. Use Newton's second law of motion to find the differential equation
that describes the motion:
- The net force acting on the ball is the sum of gravity (mg) and air resistance (which we will neglect for simplicity). So, Fnet = mg.
- Since acceleration equals force divided by mass, a = Fnet/m. In this case, m cancels out, so a = g.
- The motion equation becomes: dv/dt = g = -32.2 ft/s^2 (since we're moving upwards). This is the first differential equation.
4. Since we want to describe the ball's position (y) as well, we need
another differential equation. We can use kinematics equations:
- The velocity equation is v = v0 + at. Substitute the value of a from step 3:
dv/dt = -32.2 ft/s^2. Rewriting it as an integral:
∫dv = -32.2 ft/s^2 * dt
- Integrating with respect to time, we get v(t) = -16.1 t + C (constant of integration).
5. Now we have two equations, one for velocity and another for position:
- dv/dt = -32.2 ft/s^2 (equation 1)
- v(t) = -16.1 t + C (equation 2)
6. We need to find the constant C using the initial conditions given in
the problem. We know that initially, at time t=0, the ball's velocity is
v0:
- Equation 2 becomes v0 = -16.1 * 0 + C, which simplifies to C = v0 = 30 ft/sec (initial velocity).
7. Now we have both equations with the constants filled in:
- dv/dt = -32.2 ft/s^2 (equation 1)
- v(t) = -16.1 t + 30 ft/sec (equation 2)
8. Finally, we need to find the ball's position (y) as a function of
time:
- Use the second kinematics equation y = y0 + v0*t + ½*a*t^2 (since acceleration is constant, it can be moved outside the integral).
- Substitute the values for v0 and a:
y(t) = 3 ft + (30 ft/sec) * t + (-½ * 32.2 ft/s^2) * t^2
That's it! The differential equation describing the motion of the ball
is:
- dv/dt = -32.2 ft/s^2 (equation 1)
- v(t) = -16.1 t + 30 ft/sec (equation 2)
- y(t) = 3 ft + (30 ft/sec) * t - (16.1 t^2) ft (equation 3)
datasets:
- Locutusque/hyperion-dpo-v1.0
quantized_by: bartowski
pipeline_tag: text-generation
Llamacpp Quantizations of Hyperion-3.0-Mistral-7B-DPO
Using llama.cpp release b2440 for quantization.
Original model: https://huggingface.co/Locutusque/Hyperion-3.0-Mistral-7B-DPO
Download a file (not the whole branch) from below:
Filename | Quant type | File Size | Description |
---|---|---|---|
Hyperion-3.0-Mistral-7B-DPO-Q8_0.gguf | Q8_0 | 7.69GB | Extremely high quality, generally unneeded but max available quant. |
Hyperion-3.0-Mistral-7B-DPO-Q6_K.gguf | Q6_K | 5.94GB | Very high quality, near perfect, recommended. |
Hyperion-3.0-Mistral-7B-DPO-Q5_K_M.gguf | Q5_K_M | 5.13GB | High quality, very usable. |
Hyperion-3.0-Mistral-7B-DPO-Q5_K_S.gguf | Q5_K_S | 4.99GB | High quality, very usable. |
Hyperion-3.0-Mistral-7B-DPO-Q5_0.gguf | Q5_0 | 4.99GB | High quality, older format, generally not recommended. |
Hyperion-3.0-Mistral-7B-DPO-Q4_K_M.gguf | Q4_K_M | 4.36GB | Good quality, similar to 4.25 bpw. |
Hyperion-3.0-Mistral-7B-DPO-Q4_K_S.gguf | Q4_K_S | 4.14GB | Slightly lower quality with small space savings. |
Hyperion-3.0-Mistral-7B-DPO-IQ4_NL.gguf | IQ4_NL | 4.15GB | Good quality, similar to Q4_K_S, new method of quanting, |
Hyperion-3.0-Mistral-7B-DPO-IQ4_XS.gguf | IQ4_XS | 3.94GB | Decent quality, new method with similar performance to Q4. |
Hyperion-3.0-Mistral-7B-DPO-Q4_0.gguf | Q4_0 | 4.10GB | Decent quality, older format, generally not recommended. |
Hyperion-3.0-Mistral-7B-DPO-IQ3_M.gguf | IQ3_M | 3.28GB | Medium-low quality, new method with decent performance. |
Hyperion-3.0-Mistral-7B-DPO-IQ3_S.gguf | IQ3_S | 3.18GB | Lower quality, new method with decent performance, recommended over Q3 quants. |
Hyperion-3.0-Mistral-7B-DPO-Q3_K_L.gguf | Q3_K_L | 3.82GB | Lower quality but usable, good for low RAM availability. |
Hyperion-3.0-Mistral-7B-DPO-Q3_K_M.gguf | Q3_K_M | 3.51GB | Even lower quality. |
Hyperion-3.0-Mistral-7B-DPO-Q3_K_S.gguf | Q3_K_S | 3.16GB | Low quality, not recommended. |
Hyperion-3.0-Mistral-7B-DPO-Q2_K.gguf | Q2_K | 2.71GB | Extremely low quality, not recommended. |
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