What is the value of y in the formula shown when x = 4/5? y = 4x + √x + 0.2 – 5x y =
The Correct Answer and Explanation is:
The given formula is:
y=4x+x+0.2−5xy = 4x + \sqrt{x} + 0.2 – 5xy=4x+x+0.2−5x
We are asked to find the value of yyy when x=45x = \frac{4}{5}x=54.
Step-by-Step Calculation:
- Substitute x=45x = \frac{4}{5}x=54 into the formula:
y=4(45)+45+0.2−5(45)y = 4\left(\frac{4}{5}\right) + \sqrt{\frac{4}{5}} + 0.2 – 5\left(\frac{4}{5}\right)y=4(54)+54+0.2−5(54)
- Simplify each term:
- First, simplify 4×454 \times \frac{4}{5}4×54: 4×45=165=3.24 \times \frac{4}{5} = \frac{16}{5} = 3.24×54=516=3.2
- Next, simplify 45\sqrt{\frac{4}{5}}54. To calculate the square root, we can express 45\frac{4}{5}54 as a decimal: 45=0.8\frac{4}{5} = 0.854=0.8 Therefore: 0.8≈0.8944\sqrt{0.8} \approx 0.89440.8≈0.8944
- Then, calculate 5×455 \times \frac{4}{5}5×54: 5×45=45 \times \frac{4}{5} = 45×54=4
- Substitute these values into the equation:
y=3.2+0.8944+0.2−4y = 3.2 + 0.8944 + 0.2 – 4y=3.2+0.8944+0.2−4
- Perform the addition and subtraction:
- First, add 3.2+0.89443.2 + 0.89443.2+0.8944: 3.2+0.8944=4.09443.2 + 0.8944 = 4.09443.2+0.8944=4.0944
- Then, add 0.20.20.2 to the result: 4.0944+0.2=4.29444.0944 + 0.2 = 4.29444.0944+0.2=4.2944
- Finally, subtract 4 from the result: 4.2944−4=0.29444.2944 – 4 = 0.29444.2944−4=0.2944
Final Answer:
Thus, when x=45x = \frac{4}{5}x=54, the value of yyy is approximately 0.2944.
