Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.
Sagot :
Let's solve the given problem step-by-step.
1. Define the Function:
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = 4x - x^2 \][/tex]
2. Evaluate the Function at [tex]\( x = \frac{3}{2} \)[/tex]:
We need to substitute [tex]\( x = \frac{3}{2} \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f\left(\frac{3}{2}\right) = 4 \left(\frac{3}{2}\right) - \left(\frac{3}{2}\right)^2 \][/tex]
First, calculate [tex]\( 4 \left(\frac{3}{2}\right) \)[/tex]:
[tex]\[ 4 \left(\frac{3}{2}\right) = 4 \times \frac{3}{2} = 2 \times 3 = 6 \][/tex]
Next, calculate [tex]\( \left(\frac{3}{2}\right)^2 \)[/tex]:
[tex]\[ \left(\frac{3}{2}\right)^2 = \frac{9}{4} \][/tex]
Now, subtract [tex]\( \frac{9}{4} \)[/tex] from 6:
[tex]\[ 6 - \frac{9}{4} \][/tex]
Convert 6 to a fraction with the same denominator:
[tex]\[ 6 = \frac{24}{4} \][/tex]
So, the subtraction becomes:
[tex]\[ \frac{24}{4} - \frac{9}{4} = \frac{15}{4} \][/tex]
Therefore:
[tex]\[ f\left(\frac{3}{2}\right) = \frac{15}{4} = 3.75 \][/tex]
3. Take the Square Root of the Result:
Now, we need to find the square root of [tex]\( 3.75 \)[/tex]:
[tex]\[ \sqrt{3.75} \approx 1.9364916731037085 \][/tex]
So, the detailed steps are:
- Calculate [tex]\( f\left(\frac{3}{2}\right) \)[/tex] which results in 3.75.
- Then, take the square root of 3.75 to get approximately 1.9364916731037085.
Thus, the final result is approximately [tex]\( 1.9364916731037085 \)[/tex].
1. Define the Function:
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = 4x - x^2 \][/tex]
2. Evaluate the Function at [tex]\( x = \frac{3}{2} \)[/tex]:
We need to substitute [tex]\( x = \frac{3}{2} \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f\left(\frac{3}{2}\right) = 4 \left(\frac{3}{2}\right) - \left(\frac{3}{2}\right)^2 \][/tex]
First, calculate [tex]\( 4 \left(\frac{3}{2}\right) \)[/tex]:
[tex]\[ 4 \left(\frac{3}{2}\right) = 4 \times \frac{3}{2} = 2 \times 3 = 6 \][/tex]
Next, calculate [tex]\( \left(\frac{3}{2}\right)^2 \)[/tex]:
[tex]\[ \left(\frac{3}{2}\right)^2 = \frac{9}{4} \][/tex]
Now, subtract [tex]\( \frac{9}{4} \)[/tex] from 6:
[tex]\[ 6 - \frac{9}{4} \][/tex]
Convert 6 to a fraction with the same denominator:
[tex]\[ 6 = \frac{24}{4} \][/tex]
So, the subtraction becomes:
[tex]\[ \frac{24}{4} - \frac{9}{4} = \frac{15}{4} \][/tex]
Therefore:
[tex]\[ f\left(\frac{3}{2}\right) = \frac{15}{4} = 3.75 \][/tex]
3. Take the Square Root of the Result:
Now, we need to find the square root of [tex]\( 3.75 \)[/tex]:
[tex]\[ \sqrt{3.75} \approx 1.9364916731037085 \][/tex]
So, the detailed steps are:
- Calculate [tex]\( f\left(\frac{3}{2}\right) \)[/tex] which results in 3.75.
- Then, take the square root of 3.75 to get approximately 1.9364916731037085.
Thus, the final result is approximately [tex]\( 1.9364916731037085 \)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.