Sketch the circles. Give polar coordinates for their centers and identify their radii.

$$r = 4 \cos \theta$$

Briefly describe the significant events (and their importance) occurring at each of the following stages of fertilization: (a) Capacitation: (b) The acrosome reaction: (c) Fusion of egg and sperm plasma membranes: (d) The cortical reaction: (e) Fusion of egg and sperm nuclei:

Determine whether the statements that follow are true or false, and justify your answer: If $A^2 = I_2$, then matrix $A$ must be either $I_2$ or $-I_2$.

solve the system by the method of elimination. {3x + 4y = -26 , 7x - 5y = 11

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

$$\langle 1,2,0 \rangle \times \langle 3,0,4 \rangle$$

=___

In exercising, a weight lifter loses 0.150 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is $1.40 \times 10 ^ { 5 } \mathrm { J }$

Assuming that the latent heat of vaporization of perspiration is $2.42 \times 10 ^ { 6 } \mathrm { J } / \mathrm { kg }$ find the change in the internal energy of the weight lifter.

State the amplitude, period, vertical shift, and equation of the midline for each function. Then graph the function.

$$y = \frac { 1 } { 3 } \sin \theta + 7$$

Choose the letter of the correct term or concept below to complete the sentence. a. validity b. reliability c. norms d. intelligence e. triarchic theory f. emotional intelligence g. heritability h. cultural bias i. objective j. projective. The ability of a test to yield the same result under a variety of different circumstances is its __________.

Parallelogram ABCD has vertices

$$A \left( - 2 , - 5 \frac { 1 } { 2 } \right) , B \left( - 4 , - 5 \frac { 1 } { 2 } \right)$$

, C(-3, -2), and D(-1, -2). Find the vertices of parallelogram

$$A ^ { \prime } B ^ { \prime } C D ^ { \prime }$$

after a transformation of

$$2 \frac { 1 } { 2 }$$

units down.

Write the decimal as a percent or the percent as a decimal. 0.1

Computer algebra systems sometimes need a helping hand from human beings. Try to evaluate

$$∫(1+ln x)√1+(x ln x)^2 dx$$

with a computer algebra system. If it doesn’t return an answer, make a substitution that changes the integral into one that the CAS can evaluate.

Simplify.

$$\frac { 3 } { 8 } - \frac { 1 } { 2 } \cdot \frac { 2 } { 3 } \cdot \frac { 3 } { 4 }$$

Let S be the graph of

$$x ^ { 2 } + z ^ { 2 } + 6 z = 16$$

in 3-space. (a) The intersection of S with the xz-plane is a circle with center ___ and radius . (b) The intersection of S with the xy-plane is two lines, x= and x=___. (c)