Alright, let's work through the problem step-by-step:
We are given the equation:
[tex]\[ y = \frac{4r - 7}{h} \][/tex]
Our goal is to express [tex]\( r \)[/tex] in terms of [tex]\( h \)[/tex] and [tex]\( y \)[/tex].
Step 1: Start by eliminating the denominator [tex]\( h \)[/tex] from the right-hand side. To do this, multiply both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[ y \cdot h = 4r - 7 \][/tex]
Step 2: Next, isolate the term involving [tex]\( r \)[/tex] on one side of the equation. To do this, add 7 to both sides of the equation:
[tex]\[ y \cdot h + 7 = 4r \][/tex]
Step 3: Finally, solve for [tex]\( r \)[/tex] by dividing both sides of the equation by 4:
[tex]\[ r = \frac{y \cdot h + 7}{4} \][/tex]
Thus, the expression for [tex]\( r \)[/tex] in terms of [tex]\( h \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ r = \frac{y \cdot h + 7}{4} \][/tex]
Given specific values [tex]\( h = 2 \)[/tex] and [tex]\( y = 3 \)[/tex], we can substitute these values into our equation:
[tex]\[ r = \frac{3 \cdot 2 + 7}{4} \][/tex]
[tex]\[ r = \frac{6 + 7}{4} \][/tex]
[tex]\[ r = \frac{13}{4} \][/tex]
[tex]\[ r = 3.25 \][/tex]
Therefore, the value of [tex]\( r \)[/tex] is [tex]\( 3.25 \)[/tex].
