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ofesora Murphy le pidió a sus estudiantes que evaluaran la expresión 4x^(2)+0.5 xy^(3) cuando x=(5)/(4) y y=2. A continuación se muestran las respuestas iantes. estudiante evaluó la expresión correctamente?

ofesora Murphy le pidió a sus estudiantes que evaluaran la expresión 4x2+0.5xy3 4 x^{2}+0.5 x y^{3} cuando x=54 x=\frac{5}{4} y y=2 y=2 . A continuación se muestran las respuestas iantes.\newlineestudiante evaluó la expresión correctamente?

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Full solution

Q. ofesora Murphy le pidió a sus estudiantes que evaluaran la expresión 4x2+0.5xy3 4 x^{2}+0.5 x y^{3} cuando x=54 x=\frac{5}{4} y y=2 y=2 . A continuación se muestran las respuestas iantes.\newlineestudiante evaluó la expresión correctamente?
  1. Substitute Values: Substitute the given values of xx and yy into the expression.\newlineWe have the expression 4x2+0.5xy34x^{2} + 0.5xy^{3} and we need to substitute x=54x = \frac{5}{4} and y=2y = 2 into it.
  2. Calculate 4x24x^{2}: Calculate the value of 4x24x^{2} with x=54x = \frac{5}{4}.
    4x2=4×(54)24x^{2} = 4 \times \left(\frac{5}{4}\right)^2
    4x2=4×2516\phantom{4x^{2}} = 4 \times \frac{25}{16}
    4x2=4×2516\phantom{4x^{2}} = \frac{4 \times 25}{16}
    4x2=10016\phantom{4x^{2}} = \frac{100}{16}
    4x2=6.25\phantom{4x^{2}} = 6.25
  3. Calculate 0.5xy30.5xy^{3}: Calculate the value of 0.5xy30.5xy^{3} with x=54x = \frac{5}{4} and y=2y = 2.
    0.5xy3=0.5×54×230.5xy^{3} = 0.5 \times \frac{5}{4} \times 2^{3}
    =0.5×54×8= 0.5 \times \frac{5}{4} \times 8
    =0.5×5×84= \frac{0.5 \times 5 \times 8}{4}
    =204= \frac{20}{4}
    =5= 5
  4. Add Results: Add the results from Step 22 and Step 33 to get the final answer.\newlineFinal Answer = 6.25+56.25 + 5\newline = 11.2511.25

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