What is the sum of 52.38 divided by 16
2 answers:
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9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
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<em>Additional comment</em>
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
- 4x -5y +9 = 0
- 5x -4y +0 = 0
From the coefficients of these equations, differences of cross products are formed:
- d1 = 4(-4) -(5)(-5) = 9
- d2 = -5(0) -(-4)(9) = 36
- d3 = 9(5) -0(4) = 45
Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
- x = d2/d1 = 36/9 = 4
- y= d3/d1 = 45/9 = 5
(x, y) = (4, 5) ⇒ the number is 45.
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This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
Question:<u /> <em>Simplify the trigonometric expression sec</em><span><em>Өcos</em></span><span><em>Ө.</em></span>
For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)
Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as
.
An important property of reciprocals is that if you mutliply them together they will cancel out--take
for example.
Since sec<span>Ө is literally <em>defined</em> as the reciprocal of cos</span><span>Ө, it is evident that
</span>
For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)
Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as
An important property of reciprocals is that if you mutliply them together they will cancel out--take
Since sec<span>Ө is literally <em>defined</em> as the reciprocal of cos</span><span>Ө, it is evident that