Mixed Science

dx+ey= f---------------2

multiply equation 1 by d and equation 2 by a , to give:

adx + bdy = cd-------3

adx + aey = af--------4

Subtract equation 4 from equation 3

bdy - aey = cd-af

simplifying, we have

y(bd-ae) = cd-af

dividing both sides by bd-ae

y(bd-ae)/bd-ae = cd-af/bd-ae

y= cd-af/bd-ae

Derivation for x

ax + by = c-----------1

dx +ey = f------------2

Multiply equation1 by e and equation 2 by b, to give

aex + bey = ce-------------------3

bdx +bey = bf-------------------4

subtract equation 4 from equation 3

aex - bdx = ce- bf

Simplify the L.H.S, we have

x(ae-bd) = ce-bf

dividing both sides by ae - bd

x = ce-bf/ae-bd

Using Samuel's equation to solve simultaneous equation

2x + 3y =5-----------1

3x + 4y =7-----------2

solve for x, using x = ce-bf/ae-bd

Note, a =2, b =3, c=5, d=3, e=4, f=7

x = 5(4) - 3(7)/2(4) - 3(3)

=20 - 21/8 - 9

=-1/-1

=1

Assignment: Solve for Y using Samuel's Formula

What is acne?

Acne (acne vulgaris, common acne) is a disease of the hair follicles of the face, chest, and back that affects almost all males and females during puberty; the only exception being teenage members of a few primitive isolated tribes living in Neolithic societies. It is not caused by bacteria, although bacteria play a role in its development. It is not unusual for some women to develop acne in their mid- to late-20s.
Acne appears on the skin as...

• congested pores ("comedones"), also known as blackheads or whiteheads,
• tender red bumps also known as pimples or zits,
• pustules, and occasionally as
• cysts (deep pimples, boils).

You can do a lot to treat your acne using products available at a drugstore or cosmetic counter that do not require a prescription. However, for tougher cases of acne, you should consult a physician for treatment options.

What causes acne?

No one factor causes acne. Acne happens when sebaceous (oil) glands attached to the hair follicles are stimulated at the time of puberty by elevated levels of male hormones. Sebum (oil) is a natural substance which lubricates and protects the skin. Associated with increased oil production is a change in the manner in which the skin cells mature so that they are predisposed to clog the follicular openings or pores. The clogged hair follicle gradually enlarges, producing a bump. As the follicle enlarges, the wall may rupture, allowing irritating substances and normal skin bacteria access into the deeper layers of the skin, ultimately producing inflammation.
Inflammation near the skin's surface produces a pustule; deeper inflammation results in a papule (pimple); deeper still and it's a cyst. If the oil breaks though to the surface, the result is a "whitehead." If the oil accumulates melanin pigment or becomes oxidized, the oil changes from white to black, and the result is a "blackhead." Blackheads are therefore not dirt and do not reflect poor hygiene.
Here are some factors that don't usually play a role in acne:

• Heredity: With the exception of very severe acne, most people do not have the problem exactly as their parents did. Almost everyone has some acne at some point in their life.
• Food: Parents often tell teens to avoid pizza, chocolate, greasy and fried foods, and junk food. While these foods may not be good for overall health, they don't cause acne or make it worse. Although some recent studies have implicated milk and pure chocolate in aggravating acne, these findings are very far from established.
• Dirt: As mentioned above, "blackheads" are oxidized oil, not dirt. Sweat does not cause acne, therefore, it is not necessary to shower instantly after exercise for fear that sweat will clog pores. On the other hand, excessive washing can dry and irritate the skin.
• Stress: Some people get so upset by their pimples that they pick at them and make them last longer. Stress, however, does not play much of a direct role in causing acne.

In occasional patients, the following may be contributing factors:

• Pressure: In some patients, pressure from helmets, chin straps, collars, suspenders, and the like can aggravate acne.
• Drugs: Some medications may cause or worsen acne, such as those containing iodides, bromides, or oral or injected steroids (either the medically prescribed prednisone [Deltasone, Orasone, Prednicen-M, Liquid Pred] or the steroids that bodybuilders or athletes take). Other drugs that can cause or aggravate acne are anticonvulsant medications and lithium (Eskalith, Lithobid), which is used to treat bipolar disorder. Most cases of acne, however, are not drug related.
• Occupations: In some jobs, exposure to industrial products like cutting oils may produce acne.
• Cosmetics: Some cosmetics and skin-care products are pore clogging ("comedogenic"). Of the many available brands of skin-care products, it is important to read the list of ingredients and choose those which have water listed first or second if you are concerned about acne. These "water-based" products are usually safe.