When run at maximum power output, the motor in a self-propelled tank car can accelerate the full car (mass $M$ kg) along a horizontal track at $a$ m/s$^2$ . The tank is full at time zero, but the contents pour out of a hole in the bottom at rate $k$ kg/s thereafter. If the car is at rest at time zero and full forward power is turned on at that time , how fast will it be moving at any time $t$ before the tank is empty?

Find the Jacobian $\frac{\partial(x, y)}{\partial(u, v)} \text { or } \frac{\partial(x, y, z)}{\partial(u, v, w)}$.

$$x=u \cos v, y=u \sin v, z=w e^{u v}$$

There are currently _____ Supreme Court justices. The Chief Justice of the Supreme Court is _______.

The other justices, known as Associate Justices, are:

Find the solution of the initial value problem $y ^ { \prime } = t y ^ { 2 }$ with y(0)=1. What is the largest interval [0, b] for which the solution exists?

A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is $s(t)=96 t-16 t^{2}.$ For what time t is the ball more than 128 feet above the ground?

A sledge loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at $20.0 ^ { \circ }$ above the horizontal. The sledge moves a distance of 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. What is the mechanical energy lost due to friction?

In the following equation, which describes the fission of uranium, what do i, ii, and iii represent? $\mathrm{i}+^{235} \mathrm{Uranium} \rightarrow \mathrm{ii}+^{91} \mathrm{Krypton}+\mathrm{iii}$ (a) 1 neutron, $^{142} \mathrm{Boron}$, heat energy, (b) 1 neutron, $^{142} \mathrm{Barium}$, $^{135} \mathrm{Cesium}$, (c) 1 neutron, $^{142} \mathrm{Barium}$, kinetic energy, (d) Kinetic energy, $^{142} \mathrm{Boron}$, potential energy, (e) Potential energy, $^{142} \mathrm{Barium}$, kinetic energy.

What are some obstacles to sympatric speciation?

Solve equation $\dfrac{m}{6}=1$ and check your answer.

In how many ways can a president, a vice-president, and a secretary be selected from an organization of 32 members?

Tuan is an artist. He is painting on a large canvas that is 45 inches wide. The height of the canvas is 9 inches less than the width. What is the area of Tuan's canvas?

A 15-m-long garden hose has an inner diameter of 2.5 cm. One end is connected to a spigot; $20 ^ { \circ } \mathrm { C }$ water flows from the other end at a rate of 1.2 L/s. What is the gauge pressure at the spigot end of the hose? A. 1900 Pa B. 2700 Pa C. 4200 Pa D. 5800 Pa E. 7300 Pa

(a) Determine the radius of the smallest cation that can have (i) sixfold and (ii) eightfold coordination with the $\mathrm{Cl}^{-}$ ion (radius 181 pm). (b) Determine the radius of the smallest anion that can have (i) sixfold and (ii) eightfold coordination with the $\mathrm{Rb}^{+}$ ion (radius 149 pm).

Consider this geometric sequence: $3,6,12,24,48, \ldots$ a. What is the common ratio r? b. Call the general term of this sequence $A_{n}$. Suppose that the starting subscript for the sequence is 0. Thus, the initial term is $A_{0}=3$. What is a recursive formula for this sequence? What is a function formula for this sequence? Write both formulas in the form $"A_{n}=\ldots,$") c. Suppose the starting subscript is 1. Thus, $A_{1}=3$. What is a recursive formula for the sequence in this case? What is a function formula? (Write both formulas in the form $"A_{n}=\ldots$." d. Compare the formulas in Parts b and c. Explain similarities and differences.