Тема: Scott Adams' Blog - Dilbert

Solving the Equation: The Variables for Women’s Success in Engineering and Computing asks why there are still so few women in the critical fields of engineering and computing — and explains what we can do to make these fields open to and desirable for all employees.

The numbers are especially low for Hispanic, African American, and American Indian women. Black women make up 1 percent of the engineering workforce and 3 percent of the computing workforce, while Hispanic women hold just 1 percent of jobs in each field. American Indian and Alaska Native women make up just a fraction of a percent of each workforce.

A wording such as "an equation in x and y ", or "solve for x and y ", implies that the unknowns are as indicated: in these cases x and y.

where x 1 ,., x n are the unknowns, and c is a constant. Its solutions are the members of the inverse image

In this chapter, we will develop certain techniques that help solve problems stated in words. These techniques involve rewriting problems in the form of symbols. For example, the stated problem

and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.

In other words, we want to move everything except x (or whatever name the variable has) over to the right hand side.

That was interesting. we thought we had found a solution, but when we looked back at the question and found it wasn''t allowed!

A wording such as "an equation in x and y ", or "solve for x and y ", implies that the unknowns are as indicated: in these cases x and y.

where x 1 ,., x n are the unknowns, and c is a constant. Its solutions are the members of the inverse image

In this chapter, we will develop certain techniques that help solve problems stated in words. These techniques involve rewriting problems in the form of symbols. For example, the stated problem

and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.

For problem 1: You have two variables and two equations: x (first number), y (second number) 2*x=y+20 (two times the first = the second plus twenty) .25*x=.25*y-2 (one fourth the first = one fourth the second number minus two) Solve either equation for one variable. I will solve the first for y. (2x)-20=(y+20)-20 (subtract twenty from both sides) y=2x-20 (simplify) Now, substitute this into the other equation. .25x=.25(2x-20)-2 (where y was before I substituted in what we just found that y equaled) .25x=(.5x-5)-2 (distribute the.25 into the parentheses) .25x=.5x-7 (simplify) (.25x)-.5x=(.5x-7)-.5x (subtract.5x from both sides to get it on only one side of the equation) -.25x=-7 (simplify) .25x=7 (multiply both sides by -1 to remove negatives) x=28 (divide both sides by.25 or multiply both sides by 4) Now we plug the value for x into the equation for y. y=2x-20 (equation) y=2(28) -20 (substitute value for x) y=56-20 (multiply 28 by 2) y=36 (subtract 20 from 56) The answer is B: 28,36 For problem 2: We are given two equations to start with. I will solve the first for x. 8x-3y=3 (original equation) 8x-3y+3y=3+3y (add 3y to both sides) 8x=3y+3 (simplify) 8x/8=(3y+3)/8 (divide both sides by 8) x=(3/8)y+(3/8) Substitute this into the other equation. 3x-2y+5=0 (original equation) 3((3/8)y+(3/8))-2y+5=0 (substitute what we found for x with the x in this equation) (9/8)y+(9/8)-27+5=0 (distribute the 3 into the parentheses) -(7/8)y+9/8+5=0 (sum the two y values) -(7/8)y+(49/8)=0 (sum the fraction and 5) (-(7/8)y+(49/8))-(49/8)=0-(49/8) (subtract 49/8 from both sides) -(7/8)y=-(49/8) (simplify) (7/8)y=(49/8) (multiply both sides by -1 to remove negatives) ((7/8)y)*(8/7)=(49/8)*(8/7) (multiply both sides by 8/7 to remove the coefficient of y) y=7 (simplify) Now we plug the value for y into the equation for x x=(3/8)y+(3/8) (equation) x=(3/8)(7) +(3/8) (substitute y for what y equals) x=(21/8)+(3/8) (multiply the first constant by 7) x=3 (sum the two fractions) The answer is A:(3,7)

A wording such as "an equation in x and y ", or "solve for x and y ", implies that the unknowns are as indicated: in these cases x and y.

where x 1 ,., x n are the unknowns, and c is a constant. Its solutions are the members of the inverse image

In this chapter, we will develop certain techniques that help solve problems stated in words. These techniques involve rewriting problems in the form of symbols. For example, the stated problem

and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.

In other words, we want to move everything except x (or whatever name the variable has) over to the right hand side.

That was interesting. we thought we had found a solution, but when we looked back at the question and found it wasn't allowed!

In general, use logarithms to solve problems when the variables are in the exponents. In this case, since you are dealing with powers of e, use natural logs. So ln[3*e^2t] = ln[e^-2t], ln(3) +2t = -2t solve for t,

7

Afew examples of what you can ask Wolfram|Alpha about: Equations. solve a linear equation