Desprezando a espessura de seus lados, sabe- mos que um recipiente em formato cúbico de aresta igual a 10 cm tem capacidade de armazenar 1 litro água. Nestas condições, quantos litros de água cabem em um recipiente cúbico cuja aresta é igual a 40 cm ? (A) 120 litros (B) 4 litros (C) 64 litros (D) 640 litros

Find the probability. When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8 .

\( \leftarrow \) Use implicit differentiation to find \( \frac{\mathrm{dy}}{\mathrm{dx}} \) \[ \begin{array}{l}e^{3 \mathrm{xy}}=8 \mathrm{y}\end{array} \]

You must get from a point \( P \) on the straight shore of a lake to a stranded swimmer who is 30 m from a point \( Q \) on the shore that is 30 m from you (see figure). If you can swim at a speed of \( 2 \frac{\mathrm{~m}}{\mathrm{~s}} \) and run at a speed of \( 4 \frac{\mathrm{~m}}{\mathrm{~s}} \), at what point along the shore, x meters from Q , should you stop running and start swimming if you want to reach the swimmer in the minimum time? Complete parts (a) through (d) below. B. \( T(x)=\frac{\sqrt{900-x^{2}}}{2}+\frac{(30-x)}{4} \) C. \( T(x)=2 \sqrt{900+x^{2}}+4(30-x) \) D. \( T(x)=4 \sqrt{900+x^{2}}+16(30-x) \) b. Find the critical point of \( T \) on \( (0,30) \). x \( =\square \) (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Tarea Gionficar las siguientes form- a. \( f(x)=\left(\frac{1}{3} y^{x}\right. \) b. \( f(x)=3^{x} \) c. \( f(x)=\log _{3} x \) d. \( f(x)=\log _{\frac{1}{3}} x \)

\( \int _ { x } ^ { 0 } e ^ { 3 , x , d x } d x \)