4. Diego is thinking of two positive numbers. He says, "If we triple the first number and double the second number, the sum is \( 34 . " \) a. Write an equation that represents this clue. Then, find two possible pairs of numbers Diego could be thinking of. b. Diego then says, "If we take half of the first number and double the second, the sum is 14." Write an equation that could represent this description. c. What are Diego's two numbers? Explain or show how you know. A coordinate plane is given here, in case helpful.

Q.1.4 Determine the current overall total value of the eight tools, including the inflation (2) adjustment amount, by inserting an appropriate formula into cell D14.

Find \( \frac{d y}{d x} \) where \( y=\sec ^{-1}\left(\sqrt{3 x^{3}}\right) \)

\( \left. \begin{array} { l }{ \int _ { - 2 } ^ { 1 } | x | x ^ { 3 } d x = \int _ { - 2 } ^ { 0 } ( - x ) x ^ { 2 } d x + \int _ { - 2 } ^ { 1 } ( x ) x ^ { 2 } d x } \\ { = \int _ { - 2 } ^ { 0 } - x ^ { 3 } d x + \int _ { 0 } ^ { 1 } x ^ { 3 } d x } \end{array} \right. \)

6. Dada las curvas \( X=\left\{\begin{array}{c}x=t \\ y=e^{-t} \\ z=2 t-t^{2}\end{array}, t \in R\right. \) y \( Y=\left\{\begin{array}{c}x=2 t-1 \\ y=t^{2}+2 t, t \epsilon R \text {. Determine: } \\ z=2 t+3\end{array}\right. \) a. Las ecuaciones paramétricas de la recta tangente a la curva \( X \) en el punto A( \( 0,1,0) \) y grafique la curva, la recta tangente \( y \) la recta normal. b. Halle los valores de t, tales que la recta tangente a la curva \( Y \) sea paralela a la recta \( Z=(1,-2,2)+s(3,3,-1) ; s \in R \). Luego realice la gráfica. c. Halle los valores de t , tales que la recta tangente a la curva \( Y \) sea paralela al plano \( 5 x+4 z=3 \). Luego realice la gráfica.

1. \( y=2 \cos \left(x-\frac{\pi}{3}\right)+2 \) функциясы берілген a) Функция мәндерінің жиының көрсету. b) Қарапайым түрлендіру аркылы осы функцияның графигін салу