Question

A. Find diameter A whenx= 9..82 cm and y = 11.94 cm.B. find y when diameter A = 30.36 cm and X =23.72 cm

Answer 1

we can notice x is the sum of half DIA A and half BD

`x=(A)/(2)+(BD)/(2)`

and y is the sum of half DIA A and BD

`y=(A)/(2)+BD`

A. Find diameter A when x= 9..82 cm and y = 11.94 cm.

we replace x=9.8 and y=11.94 on the equations

`\begin{gathered} 9.8=(A)/(2)+(BD)/(2) \\ \\ 11.94=(A)/(2)+BD \end{gathered}`

now we have two equations and two unknows, then we can solve BD from the first equation

`\begin{gathered} 9.8=(A)/(2)+(BD)/(2) \\ \\ 9.8-(A)/(2)=(BD)/(2) \\ \\ BD=19.6-A \end{gathered}`

and replace on the second to find A

`11.94=(A)/(2)+(19.6-A)`

simplify

`\begin{gathered} 11.94=(A)/(2)+19.6-A \\ \\ 11.94=-(A)/(2)+19.6 \end{gathered}`

and solve for A

`\begin{gathered} 11.94-19.6=-(A)/(2) \\ \\ -7.66=-(A)/(2) \\ \\ 7.66=(A)/(2) \\ \\ A=7.66*2=15.32 \end{gathered}`

Value of Diameter A is 15.32 cm

B. find y when diameter A = 30.36 cm and X =23.72 cm

now on the initial equations for x and y we replace A and X

`\begin{gathered} 23.72=(30.36)/(2)+(BD)/(2) \\ \\ y=(30.36)/(2)+BD \end{gathered}`

we have two equations, we realize we can simplify the first equation

`\begin{gathered} 23.72=(30.36)/(2)+(BD)/(2) \\ \\ 23.72=15.18+(BD)/(2) \end{gathered}`

and we can solve BD

`\begin{gathered} 23.72-15.18=(BD)/(2) \\ 8.54=(BD)/(2) \\ \\ BD=8.54*2=17.08 \end{gathered}`

now we replace BD on the second equation

`\begin{gathered} y=(30.36)/(2)+BD \\ \\ y=15.18+17.08 \\ \\ y=32.26 \end{gathered}`

The value of y is 32.26 centimeters