id int64 1 14M | domain stringclasses 6
values | topic stringclasses 23
values | subtopic stringclasses 37
values | difficulty int64 1 8 | unit_type stringclasses 3
values | title stringlengths 14 86 | content stringlengths 203 553 | key_equations stringclasses 23
values | prerequisites stringclasses 29
values | learning_objective stringclasses 37
values |
|---|---|---|---|---|---|---|---|---|---|---|
4,901 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 1.141 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 1.141 AU one obtains T = 1.219 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,902 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 16.81 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 16.81 AU one obtains T = 68.9 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,903 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 5.539 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 5.539 AU one obtains T = 13.04 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,904 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 10.98 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 10.98 AU one obtains T = 36.36 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,905 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 24.12 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 24.12 AU one obtains T = 118.5 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,906 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 39.05 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 39.05 AU one obtains T = 244 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,907 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 13 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 13 AU one obtains T = 46.87 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,908 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 9.164 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 9.164 AU one obtains T = 27.74 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,909 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 1.116 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 1.116 AU one obtains T = 1.178 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,910 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 13.25 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 13.25 AU one obtains T = 48.26 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,911 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 2.923 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 2.923 AU one obtains T = 4.998 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,912 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 11.8 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 11.8 AU one obtains T = 40.52 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,913 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 28.6 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 28.6 AU one obtains T = 152.9 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,914 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 33.15 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 33.15 AU one obtains T = 190.8 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,915 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 23.68 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 23.68 AU one obtains T = 115.2 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,916 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 25.54 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 25.54 AU one obtains T = 129 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,917 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 13.42 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 13.42 AU one obtains T = 49.15 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,918 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 15.81 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 15.81 AU one obtains T = 62.84 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,919 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 37.22 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 37.22 AU one obtains T = 227.1 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,920 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 0.8977 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 0.8977 AU one obtains T = 0.8505 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,921 | earth_space | astronomy | kepler_third_law | 5 | worked_example | Orbital period for semi-major axis 13.89 AU | For a planet orbiting the Sun, Kepler's third law states that the square of the sidereal orbital period T (in years) equals the cube of the semi-major axis a (in AU): T² = a³. With a = 13.89 AU one obtains T = 51.75 years. The law is a direct consequence of Newtonian gravity for a central inverse-square force. | T^2 = a^3 (solar units) | newtonian gravity | Apply Kepler's third law to relate orbital period and semi-major axis. |
4,922 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.536 x + -2.225 at x = -0.761 | The linear relation y = m x + b with slope m = -1.536 and intercept b = -2.225 evaluated at x = -0.761 yields y = -1.055. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,923 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.426 x + -11.57 at x = 3.955 | The linear relation y = m x + b with slope m = 2.426 and intercept b = -11.57 evaluated at x = 3.955 yields y = -1.982. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,924 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.73 x + -9.772 at x = -9.355 | The linear relation y = m x + b with slope m = 1.73 and intercept b = -9.772 evaluated at x = -9.355 yields y = -25.95. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,925 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.523 x + 18.71 at x = 2.628 | The linear relation y = m x + b with slope m = 3.523 and intercept b = 18.71 evaluated at x = 2.628 yields y = 27.97. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,926 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.6133 x + -6.188 at x = -5.849 | The linear relation y = m x + b with slope m = 0.6133 and intercept b = -6.188 evaluated at x = -5.849 yields y = -9.775. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,927 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.849 x + -5.232 at x = -4.164 | The linear relation y = m x + b with slope m = 4.849 and intercept b = -5.232 evaluated at x = -4.164 yields y = -25.42. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,928 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.847 x + 6.98 at x = -9.409 | The linear relation y = m x + b with slope m = -1.847 and intercept b = 6.98 evaluated at x = -9.409 yields y = 24.35. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,929 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.249 x + -13.33 at x = -2.967 | The linear relation y = m x + b with slope m = 1.249 and intercept b = -13.33 evaluated at x = -2.967 yields y = -17.04. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,930 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.6847 x + 19.83 at x = -9.532 | The linear relation y = m x + b with slope m = -0.6847 and intercept b = 19.83 evaluated at x = -9.532 yields y = 26.36. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,931 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.734 x + 2.258 at x = -0.1849 | The linear relation y = m x + b with slope m = 4.734 and intercept b = 2.258 evaluated at x = -0.1849 yields y = 1.383. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,932 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.653 x + 16.85 at x = -7.366 | The linear relation y = m x + b with slope m = -2.653 and intercept b = 16.85 evaluated at x = -7.366 yields y = 36.39. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,933 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.071 x + 13.99 at x = -8.06 | The linear relation y = m x + b with slope m = 1.071 and intercept b = 13.99 evaluated at x = -8.06 yields y = 5.352. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,934 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.817 x + 19.69 at x = 1.415 | The linear relation y = m x + b with slope m = -2.817 and intercept b = 19.69 evaluated at x = 1.415 yields y = 15.7. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,935 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.214 x + -13.64 at x = 5.55 | The linear relation y = m x + b with slope m = -3.214 and intercept b = -13.64 evaluated at x = 5.55 yields y = -31.47. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,936 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.345 x + -3.955 at x = -1.83 | The linear relation y = m x + b with slope m = 2.345 and intercept b = -3.955 evaluated at x = -1.83 yields y = -8.245. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,937 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.513 x + -3.273 at x = 1.985 | The linear relation y = m x + b with slope m = 2.513 and intercept b = -3.273 evaluated at x = 1.985 yields y = 1.715. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,938 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.806 x + -5.473 at x = -7.887 | The linear relation y = m x + b with slope m = -1.806 and intercept b = -5.473 evaluated at x = -7.887 yields y = 8.771. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,939 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.848 x + 18.41 at x = 5.235 | The linear relation y = m x + b with slope m = 3.848 and intercept b = 18.41 evaluated at x = 5.235 yields y = 38.55. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,940 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.822 x + 1.425 at x = -2.157 | The linear relation y = m x + b with slope m = -1.822 and intercept b = 1.425 evaluated at x = -2.157 yields y = 5.355. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,941 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.591 x + -0.2067 at x = -0.7217 | The linear relation y = m x + b with slope m = 3.591 and intercept b = -0.2067 evaluated at x = -0.7217 yields y = -2.798. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,942 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.261 x + -2.022 at x = 8.478 | The linear relation y = m x + b with slope m = 3.261 and intercept b = -2.022 evaluated at x = 8.478 yields y = 25.63. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,943 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.224 x + -8.464 at x = 0.6533 | The linear relation y = m x + b with slope m = -3.224 and intercept b = -8.464 evaluated at x = 0.6533 yields y = -10.57. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,944 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.659 x + -1.439 at x = -6.555 | The linear relation y = m x + b with slope m = -1.659 and intercept b = -1.439 evaluated at x = -6.555 yields y = 9.438. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,945 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.073 x + -4.666 at x = 3.062 | The linear relation y = m x + b with slope m = 4.073 and intercept b = -4.666 evaluated at x = 3.062 yields y = 7.805. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,946 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.742 x + -3.588 at x = 2.728 | The linear relation y = m x + b with slope m = 4.742 and intercept b = -3.588 evaluated at x = 2.728 yields y = 9.351. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,947 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.189 x + -14.46 at x = 2.398 | The linear relation y = m x + b with slope m = 1.189 and intercept b = -14.46 evaluated at x = 2.398 yields y = -11.61. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,948 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.989 x + 3.983 at x = 4.643 | The linear relation y = m x + b with slope m = 4.989 and intercept b = 3.983 evaluated at x = 4.643 yields y = 27.15. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,949 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.455 x + -6.999 at x = -5.001 | The linear relation y = m x + b with slope m = 4.455 and intercept b = -6.999 evaluated at x = -5.001 yields y = -29.28. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,950 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.6931 x + -1.123 at x = -8.181 | The linear relation y = m x + b with slope m = 0.6931 and intercept b = -1.123 evaluated at x = -8.181 yields y = -6.793. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,951 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.297 x + 9.719 at x = 7.67 | The linear relation y = m x + b with slope m = -1.297 and intercept b = 9.719 evaluated at x = 7.67 yields y = -0.23. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,952 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.541 x + 2.082 at x = 7.269 | The linear relation y = m x + b with slope m = 1.541 and intercept b = 2.082 evaluated at x = 7.269 yields y = 13.28. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,953 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.503 x + -13.54 at x = -2.619 | The linear relation y = m x + b with slope m = 3.503 and intercept b = -13.54 evaluated at x = -2.619 yields y = -22.72. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,954 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.747 x + -12.99 at x = 8.743 | The linear relation y = m x + b with slope m = 3.747 and intercept b = -12.99 evaluated at x = 8.743 yields y = 19.76. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,955 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.214 x + -7.091 at x = -4.14 | The linear relation y = m x + b with slope m = 4.214 and intercept b = -7.091 evaluated at x = -4.14 yields y = -24.54. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,956 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.944 x + -11.72 at x = -0.7764 | The linear relation y = m x + b with slope m = 3.944 and intercept b = -11.72 evaluated at x = -0.7764 yields y = -14.78. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,957 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.55 x + 4.13 at x = 9.794 | The linear relation y = m x + b with slope m = -2.55 and intercept b = 4.13 evaluated at x = 9.794 yields y = -20.84. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,958 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.968 x + 18.91 at x = 0.004299 | The linear relation y = m x + b with slope m = 2.968 and intercept b = 18.91 evaluated at x = 0.004299 yields y = 18.92. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,959 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.888 x + 4.16 at x = -3.375 | The linear relation y = m x + b with slope m = -3.888 and intercept b = 4.16 evaluated at x = -3.375 yields y = 17.28. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,960 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.202 x + -13.63 at x = -0.7558 | The linear relation y = m x + b with slope m = 4.202 and intercept b = -13.63 evaluated at x = -0.7558 yields y = -16.8. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,961 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.625 x + -19.72 at x = -9.354 | The linear relation y = m x + b with slope m = 4.625 and intercept b = -19.72 evaluated at x = -9.354 yields y = -62.98. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,962 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.769 x + 14.68 at x = 9.911 | The linear relation y = m x + b with slope m = 1.769 and intercept b = 14.68 evaluated at x = 9.911 yields y = 32.21. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,963 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.622 x + -17.19 at x = -1.658 | The linear relation y = m x + b with slope m = 3.622 and intercept b = -17.19 evaluated at x = -1.658 yields y = -23.19. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,964 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.4 x + 8.639 at x = -7.58 | The linear relation y = m x + b with slope m = -2.4 and intercept b = 8.639 evaluated at x = -7.58 yields y = 26.83. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,965 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.766 x + 5.884 at x = 0.6834 | The linear relation y = m x + b with slope m = 2.766 and intercept b = 5.884 evaluated at x = 0.6834 yields y = 7.774. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,966 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.763 x + -0.7677 at x = 4.521 | The linear relation y = m x + b with slope m = -4.763 and intercept b = -0.7677 evaluated at x = 4.521 yields y = -22.3. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,967 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.07 x + -4.064 at x = 6.446 | The linear relation y = m x + b with slope m = -2.07 and intercept b = -4.064 evaluated at x = 6.446 yields y = -17.41. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,968 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.688 x + -5.465 at x = 4.332 | The linear relation y = m x + b with slope m = 2.688 and intercept b = -5.465 evaluated at x = 4.332 yields y = 6.179. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,969 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.1156 x + 5.985 at x = -1.428 | The linear relation y = m x + b with slope m = 0.1156 and intercept b = 5.985 evaluated at x = -1.428 yields y = 5.82. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,970 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.759 x + -14.16 at x = -4.75 | The linear relation y = m x + b with slope m = -3.759 and intercept b = -14.16 evaluated at x = -4.75 yields y = 3.697. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,971 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.252 x + 10.14 at x = -7.764 | The linear relation y = m x + b with slope m = 3.252 and intercept b = 10.14 evaluated at x = -7.764 yields y = -15.11. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,972 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.31 x + -3.484 at x = -3.203 | The linear relation y = m x + b with slope m = -3.31 and intercept b = -3.484 evaluated at x = -3.203 yields y = 7.12. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,973 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.13 x + 11.82 at x = -5.798 | The linear relation y = m x + b with slope m = 4.13 and intercept b = 11.82 evaluated at x = -5.798 yields y = -12.12. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,974 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.029 x + 5.681 at x = -8.519 | The linear relation y = m x + b with slope m = -4.029 and intercept b = 5.681 evaluated at x = -8.519 yields y = 40. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,975 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.992 x + -0.3369 at x = -5.105 | The linear relation y = m x + b with slope m = 3.992 and intercept b = -0.3369 evaluated at x = -5.105 yields y = -20.72. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,976 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.4 x + -8.188 at x = -1.107 | The linear relation y = m x + b with slope m = -2.4 and intercept b = -8.188 evaluated at x = -1.107 yields y = -5.533. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,977 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.874 x + 7.982 at x = 1.365 | The linear relation y = m x + b with slope m = 2.874 and intercept b = 7.982 evaluated at x = 1.365 yields y = 11.9. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,978 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.9443 x + 10.45 at x = -7.04 | The linear relation y = m x + b with slope m = 0.9443 and intercept b = 10.45 evaluated at x = -7.04 yields y = 3.806. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,979 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.116 x + -11.16 at x = -2.583 | The linear relation y = m x + b with slope m = -2.116 and intercept b = -11.16 evaluated at x = -2.583 yields y = -5.694. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,980 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.373 x + -8.351 at x = 8.896 | The linear relation y = m x + b with slope m = -1.373 and intercept b = -8.351 evaluated at x = 8.896 yields y = -20.56. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,981 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.417 x + 5.356 at x = -0.4943 | The linear relation y = m x + b with slope m = -3.417 and intercept b = 5.356 evaluated at x = -0.4943 yields y = 7.045. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,982 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.6014 x + -8.205 at x = 4.875 | The linear relation y = m x + b with slope m = -0.6014 and intercept b = -8.205 evaluated at x = 4.875 yields y = -11.14. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,983 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.951 x + -14.14 at x = -4.153 | The linear relation y = m x + b with slope m = 1.951 and intercept b = -14.14 evaluated at x = -4.153 yields y = -22.24. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,984 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.158 x + 5.47 at x = -9.44 | The linear relation y = m x + b with slope m = -1.158 and intercept b = 5.47 evaluated at x = -9.44 yields y = 16.4. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,985 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.883 x + -7.882 at x = 1.685 | The linear relation y = m x + b with slope m = -2.883 and intercept b = -7.882 evaluated at x = 1.685 yields y = -12.74. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,986 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.406 x + 8.846 at x = 4.909 | The linear relation y = m x + b with slope m = -2.406 and intercept b = 8.846 evaluated at x = 4.909 yields y = -2.965. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,987 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.961 x + -3.766 at x = 2.369 | The linear relation y = m x + b with slope m = 4.961 and intercept b = -3.766 evaluated at x = 2.369 yields y = 7.988. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,988 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.296 x + -6.231 at x = -6.882 | The linear relation y = m x + b with slope m = -3.296 and intercept b = -6.231 evaluated at x = -6.882 yields y = 16.45. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,989 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.526 x + -7.428 at x = -2.513 | The linear relation y = m x + b with slope m = 3.526 and intercept b = -7.428 evaluated at x = -2.513 yields y = -16.29. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,990 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.654 x + -0.5902 at x = -6.618 | The linear relation y = m x + b with slope m = 3.654 and intercept b = -0.5902 evaluated at x = -6.618 yields y = -24.77. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,991 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.2524 x + -12.98 at x = 7.943 | The linear relation y = m x + b with slope m = 0.2524 and intercept b = -12.98 evaluated at x = 7.943 yields y = -10.98. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,992 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.858 x + 17.88 at x = -3.153 | The linear relation y = m x + b with slope m = -4.858 and intercept b = 17.88 evaluated at x = -3.153 yields y = 33.19. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,993 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.907 x + -11.03 at x = -4.434 | The linear relation y = m x + b with slope m = -1.907 and intercept b = -11.03 evaluated at x = -4.434 yields y = -2.573. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,994 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.78 x + 11.57 at x = 3 | The linear relation y = m x + b with slope m = 2.78 and intercept b = 11.57 evaluated at x = 3 yields y = 19.91. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,995 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.435 x + -1.627 at x = 8.254 | The linear relation y = m x + b with slope m = -1.435 and intercept b = -1.627 evaluated at x = 8.254 yields y = -13.47. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,996 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.063 x + 13.6 at x = 6.915 | The linear relation y = m x + b with slope m = 4.063 and intercept b = 13.6 evaluated at x = 6.915 yields y = 41.69. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,997 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.831 x + 0.9647 at x = -5.433 | The linear relation y = m x + b with slope m = 2.831 and intercept b = 0.9647 evaluated at x = -5.433 yields y = -14.41. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,998 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.975 x + 6.57 at x = -2.03 | The linear relation y = m x + b with slope m = -2.975 and intercept b = 6.57 evaluated at x = -2.03 yields y = 12.61. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
4,999 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.012 x + -6.819 at x = -8.656 | The linear relation y = m x + b with slope m = -4.012 and intercept b = -6.819 evaluated at x = -8.656 yields y = 27.91. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
5,000 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.5328 x + 1.39 at x = 4.825 | The linear relation y = m x + b with slope m = 0.5328 and intercept b = 1.39 evaluated at x = 4.825 yields y = 3.961. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.