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Answer :
Sure, let's solve the problem step-by-step.
### Part (a)
We are given the length of a Brazilian snake as a function of time [tex]\( m \)[/tex] months after birth, which is [tex]\( L(m) = 3(m - 8) - 5 \)[/tex] inches.
We need to find out how old the snake is when it is 3 feet 6 inches long.
First, we need to convert 3 feet 6 inches to just inches because our function for [tex]\( L(m) \)[/tex] is in inches.
There are 12 inches in a foot, so:
[tex]\[ 3 \text{ feet} = 3 \times 12 = 36 \text{ inches} \][/tex]
[tex]\[ 3 \text{ feet 6 inches} = 36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches} \][/tex]
Next, we need to set [tex]\( L(m) \)[/tex] equal to 42 inches and solve for [tex]\( m \)[/tex]:
[tex]\[ L(m) = 42 \][/tex]
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
So the equation we need to solve is:
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
### Part (b)
Now let's solve the equation to find [tex]\( m \)[/tex]:
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
First, we simplify the equation step-by-step:
1. Distribute the 3:
[tex]\[ 3m - 24 - 5 = 42 \][/tex]
2. Combine the constants on the left side:
[tex]\[ 3m - 29 = 42 \][/tex]
3. Add 29 to both sides:
[tex]\[ 3m = 71 \][/tex]
4. Divide both sides by 3:
[tex]\[ m = \frac{71}{3} \approx 23.67 \][/tex]
So, the snake is approximately 23.67 months old when it is 3 feet 6 inches long.
In summary:
- The equation to solve is [tex]\( 3(m - 8) - 5 = 42 \)[/tex].
- The snake is approximately 23.67 months old when it is 42 inches (3 feet 6 inches) long.
### Part (a)
We are given the length of a Brazilian snake as a function of time [tex]\( m \)[/tex] months after birth, which is [tex]\( L(m) = 3(m - 8) - 5 \)[/tex] inches.
We need to find out how old the snake is when it is 3 feet 6 inches long.
First, we need to convert 3 feet 6 inches to just inches because our function for [tex]\( L(m) \)[/tex] is in inches.
There are 12 inches in a foot, so:
[tex]\[ 3 \text{ feet} = 3 \times 12 = 36 \text{ inches} \][/tex]
[tex]\[ 3 \text{ feet 6 inches} = 36 \text{ inches} + 6 \text{ inches} = 42 \text{ inches} \][/tex]
Next, we need to set [tex]\( L(m) \)[/tex] equal to 42 inches and solve for [tex]\( m \)[/tex]:
[tex]\[ L(m) = 42 \][/tex]
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
So the equation we need to solve is:
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
### Part (b)
Now let's solve the equation to find [tex]\( m \)[/tex]:
[tex]\[ 3(m - 8) - 5 = 42 \][/tex]
First, we simplify the equation step-by-step:
1. Distribute the 3:
[tex]\[ 3m - 24 - 5 = 42 \][/tex]
2. Combine the constants on the left side:
[tex]\[ 3m - 29 = 42 \][/tex]
3. Add 29 to both sides:
[tex]\[ 3m = 71 \][/tex]
4. Divide both sides by 3:
[tex]\[ m = \frac{71}{3} \approx 23.67 \][/tex]
So, the snake is approximately 23.67 months old when it is 3 feet 6 inches long.
In summary:
- The equation to solve is [tex]\( 3(m - 8) - 5 = 42 \)[/tex].
- The snake is approximately 23.67 months old when it is 42 inches (3 feet 6 inches) long.
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