Sure, let's solve for [tex]\( s \)[/tex] in each of the given equations step by step.
### Question 1
The formula provided is:
[tex]\[ A = \frac{1}{36} s^2 \][/tex]
We are given that [tex]\( A = 16 \)[/tex]. Now we need to solve for [tex]\( s \)[/tex].
Step 1: Substitute [tex]\( A = 16 \)[/tex] into the equation.
[tex]\[ 16 = \frac{1}{36} s^2 \][/tex]
Step 2: Eliminate the fraction by multiplying both sides of the equation by 36.
[tex]\[ 16 \times 36 = s^2 \][/tex]
[tex]\[ 576 = s^2 \][/tex]
Step 3: Solve for [tex]\( s \)[/tex] by taking the square root of both sides.
[tex]\[ s = \sqrt{576} \][/tex]
[tex]\[ s = 24 \][/tex]
Therefore, the value of [tex]\( s \)[/tex] when [tex]\( A = 16 \)[/tex] is [tex]\( s = 24 \)[/tex].
### Question 2
The formula provided is:
[tex]\[ A = 4 s^2 \][/tex]
We are given that [tex]\( A = 49 \)[/tex]. Now we need to solve for [tex]\( s \)[/tex].
Step 1: Substitute [tex]\( A = 49 \)[/tex] into the equation.
[tex]\[ 49 = 4 s^2 \][/tex]
Step 2: Isolate [tex]\( s^2 \)[/tex] by dividing both sides of the equation by 4.
[tex]\[ \frac{49}{4} = s^2 \][/tex]
[tex]\[ 12.25 = s^2 \][/tex]
Step 3: Solve for [tex]\( s \)[/tex] by taking the square root of both sides.
[tex]\[ s = \sqrt{12.25} \][/tex]
[tex]\[ s = 3.5 \][/tex]
Therefore, the value of [tex]\( s \)[/tex] when [tex]\( A = 49 \)[/tex] is [tex]\( s = 3.5 \)[/tex].
### Summary
- For [tex]\( A = \frac{1}{36} s^2 \)[/tex] and [tex]\( A = 16 \)[/tex], the value of [tex]\( s \)[/tex] is [tex]\( 24 \)[/tex].
- For [tex]\( A = 4 s^2 \)[/tex] and [tex]\( A = 49 \)[/tex], the value of [tex]\( s \)[/tex] is [tex]\( 3.5 \)[/tex].
