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Boyd Griffin
12/11/2023 · Junior High School
Find the soltuion to the system \( \left \{ \begin{array} { l } { a _ { 1 } x + b _ { 1 } y + c _ { 1 } z = - 2 } \\ { a _ { 2 } x + b _ { 2 } y + c _ { 2 } z = - 3 } \\ { a _ { 3 } x + b _ { 3 } y + c _ { 3 } z = - 2 } \end{array} \right . \)
given the inverse for the martix \( \left [ \begin{array} { l } { a _ { 1 } b _ { 1 } c _ { 1 } } \\ { a _ { 2 } b _ { 2 } c _ { 2 } } \\ { a _ { 3 } b _ { 3 } c _ { 3 } } \end{array} \right ] \) is
\( \left [ \begin{array} { c c c } { - 3 } & { - 3 } & { 7 } \\ { - 1 } & { - 1 } & { 2 } \\ { 2 } & { 1 } & { - 5 } \end{array} \right ] \)
\(\left [ \begin{array} { l } { x } \\ { y } \\ { z } \end{array} \right ] = \)
\(\begin{bmatrix} - 2\\ - 3\\ - 2 \end{bmatrix} \)
Required information
In 1899 Charles M. "Mile a Minute" Murphy set a record for speed on a bicycle by pedaling for a mile at an average of\( 62.3 \)mi/h (\( 27.8 m / s \)) on a track of planks set over railroad ties in the draft of a Long Island Railroad train. In\( 1985 \), a record was set for this type of "motor pacing" by Olympic cyclist John Howard who pedaled at\( 152.2 mi / h ( 68.04 m / s \)) in the wake of a race car at Bonneville Salt Flats. The race car had a modified tail assembly designed to reduce the air drag on the cyclist. Assume that the mass of bicycle plus rider is\( 71.8 kg \)in each case.
What was the kinetic energy of Howard and his bicycle?
\(\square \)kJ
What is the value of\( x \)?
Enter your answer in the box.
\( x = \square \)
Fill in the blank to make equivalent rational expressions.
\( \frac { 9 x } { x - 8 } = \frac { \square } { ( x - 8 ) ( x - 4 ) } \)
The length of a spring increases by\( 9.30 cm \)from its relaxed length when a mass of\( 1.40 kg \)is hanging in equilibrium from the spring.
What is the spring constant?
\(\square \)\( N / cm\)
Required information A 64.9 - kg woman takes 5.10s to run up a flight of stairs. The landing at the top of the stairs is 5.00m above her starting place.
What would be the efficiency of the woman's body If her average power output while she is running is equal to her average power input-the rate at which chemical energy in food or stored fat is used?
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