Final Answer:
y(2) = 32 - 2 - 32/5 - 11 = -19.6
Step-by-step explanation:
To find the value of y(2), substitute x = 2 into the equation y = 4x⁵ - (2/x⁷) + 16x⁶/⁵ - 11.
Start by evaluating each term separately after substituting x = 2:
4x⁵ = 4 * (2⁵) = 4 * 32 = 128.
2/x⁷ = 2/(2⁷) = 2/128 = 1/64.
16x⁶/⁵ = 16 * (2^(6/5)) = 16 * 2.297 = 36.752 (approximated to 36.75 for simplicity).
Finally, 11 remains unchanged.
Now, substitute these values into the equation
y = 4x⁵ - (2/x⁷) + 16x⁶/⁵ - 11:
y(2) = 128 - 1/64 + 36.75 - 11
y(2)= 127.984375 - 0.015625 + 36.75 - 11
y(2)= 127.96875 + 25.75 - 11 = 152.71875 - 11 = -19.6.
This method of substitution and evaluation is fundamental in solving equations and understanding how variables impact the resulting output. It provides a systematic way to calculate specific values or points of interest within mathematical models, enabling a deeper comprehension of their behavior and characteristics across different input values.