coeducational (coed)
(adjective)
A college that has both male and female students.
Examples of coeducational (coed) in the following topics:
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Education and Unequal Treatment in the Classroom
- In the 1970s and 1980s, some of these coordinate colleges were absorbed into the larger university to create coeducational (coed) universities with both men and women.
- Today, five still operate as women's-only colleges, Radcliffe no longer accepts students, and Vassar is coeducational.
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Women and Education
- The University of Iowa became the first coeducational public or state university in the United States in 1855, and for much of the next century, public universities (and land-grant universities in particular) would lead the way in mixed-gender higher education.
- There also were many private coeducational universities founded in the nineteenth century, especially west of the Mississippi River.
- Notable examples include the prestigious Seven Sisters; within this association of colleges, Vassar College is now coeducational and Radcliffe College has merged with Harvard University.
- Other notable women's colleges that have become coeducational include Wheaton College in Massachusetts; Ohio Wesleyan Female College in Ohio; Skidmore College, Wells College, and Sarah Lawrence College in New York state; Goucher College in Maryland; and Connecticut College.
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The Acetyl-CoA Pathway
- The acetyl-CoA pathway utilizes carbon dioxide as a carbon source and often times, hydrogen as an electron donor to produce acetyl-CoA.
- Acetyl-CoA synthetase is a class of enzymes that is key to the acetyl-CoA pathway.
- The acetyl-CoA synthetase functions in combining the carbon monoxide and a methyl group to produce acetyl-CoA. .
- The ability to utilize the acetyl-CoA pathway is advantageous due to the ability to utilize both hydrogen and carbon dioxide to produce acetyl-CoA.
- Describe the role of the carbon monoxide dehydrogenase and acetyl-CoA synthetase in the acetyl-CoA pathway
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Trigonometric Limits
- $\displaystyle{\lim_{x \to 0} \left ( \frac{1}{\cos x} \right ) = \frac{1}{1} = 1}$
- This equation can be proven with the first limit and the trigonometric identity $1 - \cos^2 x = \sin^2 x$.
- $\displaystyle{\frac{(1−\cos x)(1+\cos x)}{x(1+\cos x)}=\frac{(1−\cos^2x)}{x(1+\cos x)}=\frac{\sin^2x}{x(1+\cos x)}= \frac{\sin x}{x} \cdot \frac{\sin x}{1+\cos x}}$
- $\displaystyle{\lim_{x \to 0}\left ( \frac{\sin x}{x} \frac{\sin x}{1 + \cos x} \right ) = \left (\lim_{x \to 0} \frac{\sin x}{x} \right ) \left ( \lim_{x \to 0} \frac{\sin x}{1 + \cos x} \right ) = \left (1 \right )\left (\frac{0}{2} \right )= 0}$
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Trigonometric Integrals
- \\ \int\sin^3 {ax}\;\mathrm{d}x = \frac{\cos 3ax}{12a} - \frac{3 \cos ax}{4a} +C\!
- $\int\cos^2 {ax}\;\mathrm{d}x = \frac{x}{2} + \frac{1}{4a} \sin 2ax +C = \frac{x}{2} + \frac{1}{2a} \sin ax\cos ax +C$
- $\int\cos^n ax\;\mathrm{d}x = \frac{\cos^{n-1} ax\sin ax}{na} + \frac{n-1}{n}\int\cos^{n-2} ax\;\mathrm{d}x \qquad\mbox{(for }n>0\mbox{)}$
- $\int x^2\cos^2 {ax}\;\mathrm{d}x = \frac{x^3}{6} + \left( \frac {x^2}{4a} - \frac{1}{8a^3} \right) \sin 2ax + \frac{x}{4a^2} \cos 2ax +C$
- Two simple examples of such integrals are $\int \sin^k x \cos x \; \mathrm d x$ and $\int \cos^k x \sin x\; \mathrm d x$ , which can be solved used the substitutions $u = \sin x$ and $u = \cos x$ , respectively.
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Double and Half Angle Formulae
- Deriving the double-angle formula for sine begins with the sum formula that was introduced previously: $\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$.
- $\displaystyle{ \begin{aligned} \sin(\theta + \theta) &= \sin \theta \cos \theta + \cos \theta \sin \theta \\ \sin(2\theta) &= 2\sin \theta \cos \theta \end{aligned} }$
- $\displaystyle{ \begin{aligned} \cos{\left(2\theta \right)} &= \cos^2 \theta - \sin^2 \theta \\ &= \left(1- \sin^2 \theta \right) - \sin^2 \theta \\ &= 1- 2\sin^2 \theta \end{aligned} }$
- $\displaystyle{ \begin{aligned} \cos{\left(2\theta\right)} &= \cos^2 \theta - \sin^2 \theta \\ &= \cos^2 \theta - \left(1- \cos^2 \theta \right) \\ &= 2 \cos^2 \theta -1 \end{aligned} }$
- $\displaystyle{ \tan{\left(\frac{\alpha}{2}\right)} = \pm \sqrt{\frac{1 - \cos \alpha}{1 + \cos \alpha}} }$
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Acetyl CoA to CO2
- The acetyl carbons of acetyl CoA are released as carbon dioxide in the citric acid cycle.
- Acetyl CoA links glycolysis and pyruvate oxidation with the citric acid cycle.
- In the presence of oxygen, acetyl CoA delivers its acetyl group to a four-carbon molecule, oxaloacetate, to form citrate, a six-carbon molecule with three carboxyl groups.
- For each molecule of acetyl CoA that enters the citric acid cycle, two carbon dioxide molecules are released, removing the carbons from the acetyl group.
- Describe the fate of the acetyl CoA carbons in the citric acid cycle
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The 3-Hydroxypropionate Cycle
- Specifically, in this cycle, the carbon dioxide is fixed by acetyl-CoA and propionyl-CoA carboxylases.
- This process results in the formation of malyl-CoA which is further split into acetyl-CoA and glyoxylate.
- Propionyl-CoA carboxylase is an enzyme that functions in the carboxylation of propionyl CoA.
- The acetyl-CoA carboxylase utilized in this cycle is biotin-dependent as well and catalyzes the carboxylation of acetyl-CoA to malonyl-CoA.
- This pathway produces pyruvate via conversion of bicarbonate and also results in the production of intermediates such as acetyl-CoA, gloxylate and succinyl-CoA.
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Angle Addition and Subtraction Formulae
- $\begin{aligned} \cos(\alpha + \beta) &= \cos \alpha \cos \beta - \sin \alpha \sin \beta \\ \cos(\alpha - \beta) &= \cos \alpha \cos \beta + \sin \alpha \sin \beta \end{aligned}$
- $\begin{aligned} \sin(\alpha + \beta) &= \sin \alpha \cos \beta + \cos \alpha \sin \beta \\ \sin(\alpha - \beta) &= \sin \alpha \cos \beta - \cos \alpha \sin \beta \end{aligned}$
- Apply the formula $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$:
- $\displaystyle{ \cos{\left(\frac{5\pi}{4} - \frac{\pi}{6}\right)} = \cos{\left(\frac{5\pi}{4}\right)} \cos{\left(\frac{\pi}{6}\right)} + \sin{\left(\frac{5\pi}{4}\right)} \sin{\left(\frac{\pi}{6}\right)} }$
- $\sin(45^{\circ} - 30^{\circ}) = \sin (45^{\circ}) \cos (30^{\circ}) - \cos (45^{\circ}) \sin (30^{\circ})$
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Introduction to kinds of graphs
- Figure 3.2 is an example of a binary (as opposed to a signed or ordinal or valued) and directed (as opposed to a co-occurrence or co-presence or bonded-tie) graph.
- Figure 3.3 is an example of a "co-occurrence" or "co-presence" or "bonded-tie" graph that is binary and undirected (or simple).