Solve Using Cramer's Rule $W _ { 1 }$ And $W _ { 2 }$

question 101

Multiple Choice

Solve using Cramer's Rule.
-Linear systems occur in the design of roof trusses for new homes and buildings. The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 109-pound force is applied at the peak of the truss, then the forces or weights $W _ { 1 }$ and $W _ { 2 }$ exerted parallel to each rafter of the truss are determined by the following linear system of equations. Solve the system to find $W _ { 1 }$ and $W _ { 2 }$ .

$W _ { 1 } + \sqrt { 2 } W _ { 2 } = 218$

$\sqrt { 3 } W _ { 1 } - \sqrt { 2 } W _ { 2 } = 0$

• A) \(W _ { 1 } = 109 \mathrm { lb } ; \mathrm { W } _ { 2 } = 133.5 \mathrm { lb }\)
• B) \(\mathrm { W } _ { 1 } = 79.79 \mathrm { lb } ; \mathrm { W } _ { 2 } = 97.73 \mathrm { lb }\)
• C) \(\mathrm { W } _ { 1 } = 39.9 \mathrm { lb } ; \mathrm { W } _ { 2 } = 48.86 \mathrm { lb }\)
• D) \(\mathrm { W } _ { 1 } = 97.73 \mathrm { lb } ; \mathrm { W } _ { 2 } = 79.79 \mathrm { lb }\)

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Definitions:

Corn

A cereal plant that yields large kernels on a cob, used for food for humans and livestock, and as a raw material in industry.

Linear

Pertaining to a straight-line relationship in mathematics or economics, often used to describe a direct proportionality between variables.

Substitutes In Production

Products that can be produced using the same resources or processes as another product, allowing producers to switch between them based on market demand or cost considerations.

Fixed Resources

Assets and inputs in the production process that cannot be easily increased or decreased in the short term, such as land and machinery.