Get expert advice and insights on any topic with IDNLearn.com. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Sagot :
Sure, let's find the value of [tex]\( f\left(\frac{1}{3}\right) \)[/tex] for the function [tex]\( f(x) = 18x^2 + 30x + 2 \)[/tex].
1. Substitute [tex]\( x = \frac{1}{3} \)[/tex] into the function:
[tex]\[ f\left(\frac{1}{3}\right) = 18 \left(\frac{1}{3}\right)^2 + 30 \left(\frac{1}{3}\right) + 2 \][/tex]
2. Calculate [tex]\( \left(\frac{1}{3}\right)^2 \)[/tex]:
[tex]\[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \][/tex]
3. Multiply 18 by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ 18 \times \frac{1}{9} = 2 \][/tex]
4. Multiply 30 by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ 30 \times \frac{1}{3} = 10 \][/tex]
5. Add the results together:
[tex]\[ f\left(\frac{1}{3}\right) = 2 + 10 + 2 \][/tex]
[tex]\[ f\left(\frac{1}{3}\right) = 14 \][/tex]
So, the value of [tex]\( f\left(\frac{1}{3}\right) \)[/tex] is:
[tex]\[ f\left(\frac{1}{3}\right) = 14 \][/tex]
1. Substitute [tex]\( x = \frac{1}{3} \)[/tex] into the function:
[tex]\[ f\left(\frac{1}{3}\right) = 18 \left(\frac{1}{3}\right)^2 + 30 \left(\frac{1}{3}\right) + 2 \][/tex]
2. Calculate [tex]\( \left(\frac{1}{3}\right)^2 \)[/tex]:
[tex]\[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \][/tex]
3. Multiply 18 by [tex]\( \frac{1}{9} \)[/tex]:
[tex]\[ 18 \times \frac{1}{9} = 2 \][/tex]
4. Multiply 30 by [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[ 30 \times \frac{1}{3} = 10 \][/tex]
5. Add the results together:
[tex]\[ f\left(\frac{1}{3}\right) = 2 + 10 + 2 \][/tex]
[tex]\[ f\left(\frac{1}{3}\right) = 14 \][/tex]
So, the value of [tex]\( f\left(\frac{1}{3}\right) \)[/tex] is:
[tex]\[ f\left(\frac{1}{3}\right) = 14 \][/tex]
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.