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{:[h(t)={[sqrt(17 t),","quad t=17],[-(34 )/(t),","quad t=19],[23-t,","quad t!=17","19]:}],[h(17)=]:}

h(t)={17tamp;,t=17−34tamp;,t=1923−tamp;,t≠17,19h(17)=□ \begin{array}{l}h(t)=\left\{\begin{array}{cl}\sqrt{17 t} & , \quad t=17 \\ -\frac{34}{t} & , \quad t=19 \\ 23-t & , \quad t \neq 17,19\end{array}\right. \\ h(17)=\square\end{array}

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Full solution

Q. h(t)={17t,t=17−34t,t=1923−t,t≠17,19h(17)=□ \begin{array}{l}h(t)=\left\{\begin{array}{cl}\sqrt{17 t} & , \quad t=17 \\ -\frac{34}{t} & , \quad t=19 \\ 23-t & , \quad t \neq 17,19\end{array}\right. \\ h(17)=\square\end{array}
  1. Identify the correct piece: Identify the correct piece of the piecewise function to use for t=17 t = 17 .\newlineThe function h(t) h(t) is defined differently for different values of t t . Since we are looking for h(17) h(17) , we need to use the piece of the function that is defined for t=17 t = 17 .
  2. Use the correct piece: Use the correct piece of the piecewise function to calculate h(17)h(17).\newlineThe piece of the function for t=17t = 17 is h(t)=17th(t) = \sqrt{17t}. We substitute tt with 1717 to get h(17)=17×17h(17) = \sqrt{17 \times 17}.
  3. Perform the calculation: Perform the calculation. h(17)=17×17=289=17h(17) = \sqrt{17 \times 17} = \sqrt{289} = 17.

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