Numerade

Questions asked

INSTANT ANSWER

Mark each statement True or False. Justify each answer. a. A linear transformation is a special type of function. b. If $A$ is a $3 \times 5$ matrix and $T$ is a transformation defined by $T(\mathbf{x})=A \mathbf{x},$ then the domain of $T$ is $\mathbb{R}^{3}$. c. If $A$ is an $m \times n$ matrix, then the range of the transformation $\mathbf{x} \mapsto A \mathbf{x}$ is $\mathbb{R}^{m}$ . d. Every linear transformation is a matrix transformation. e. A transformation $T$ is linear if and only if $T\left(c_{1} \mathbf{v}_{1}+\right.$ $c_{2} \mathbf{v}_{2} )=c_{1} T\left(\mathbf{v}_{1}\right)+c_{2} T\left(\mathbf{v}_{2}\right)$ for all $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in the domain of $T$ and for all scalars $c_{1}$ and $c_{2} .$

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ANSWERED

Umar Sohail Qureshi

Numerade educator

Suppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at $v=0.80 c$ and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship's frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?

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INSTANT ANSWER

An explorer is captured by a group of cannibals. There are two types of cannibals—those who always tell the truth and those who always lie. The cannibals will barbecue the explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He is allowed to ask the cannibal exactly one question. a) Explain why the question “Are you a liar?” does not work. b) Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth.

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ANSWERED

Bryan Valdivia

Numerade educator

When a population has a gene with four alleles circulating, how many possible genotypes are there? a. 3 b. 6 c. 10 d. 16

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ANSWERED

Tracy Tourville

Numerade educator

Write the two-resonance structures for the acetate ion

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ANSWERED

Leon Druch

Numerade educator

The average prison sentence for a person convicted of second-degree murder is 15 years. If the sentences are normally distributed with a standard deviation of 2.1 years, find these probabilities: a. A prison sentence is greater than 18 years. b. A prison sentence is less than 13 years.

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INSTANT ANSWER

Express each of these statements using logical operators, predicates, and quantifiers. a) Some propositions are tautologies. b) The negation of a contradiction is a tautology. c) The disjunction of two contingencies can be a tautology. d) The conjunction of two tautologies is a tautology.

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ANSWERED

Stephen Ho

Numerade educator

Your laboratory instructor gives you a mixture of 4 -methylphenol, benzoic acid, and toluene. Assume that you have available common laboratory acids, bases, and solvents and explain how you would proceed to separate this mixture by making use of the solubility differences of its components.

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INSTANT ANSWER

A 10-kg block is attached to spring A and connected to spring B by a cord and pulley. The block is held in the position shown with both springs unstretched when the support is removed and the block is released with no initial velocity. Knowing that the constant of each spring is 2 kN/m, determine (a) the velocity of the block after it has moved down 50 mm, (b) the maximum velocity achieved by the block.

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ANSWERED

Leon Druch

Numerade educator

In Exercises $1-4,$ find the $(x, y)$ pair for the value of the parameter. $$x=t^{3}-4 t \text { and } y=\sqrt{t+1} \text { for } t=3$$

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Heather S.