Answer:
Step-by-step explanation:
P=5/12×2/12=5/72
Answer:
Step-by-step explanation:
A product is formed by multiplying the factors. Here, you want the product of -2 and x, so that is indicated as ...
-2x
You want that product greater than 30. The symbol for "greater than" is >, so you have ...
-2x > 30 . . . . the desired inequality
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The most straightforward way to solve this is to divide by the coefficient of x. Because that is negative, you must reverse the inequality symbol from "greater than" to "less than."
x < 30/(-2)
x < -15 . . . . . . the desired solution
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<em>Additional comment</em>
It may not be clear why multiplying or dividing an inequality causes the symbol to be reversed. You can think of it as reflecting the inequality over the point x=0 on the number line. Where larger numbers were on the right, they get reflected to points farther left, so as negative numbers, they are smaller numbers.
Consider ...
1 < 2
-1 > -2
If <em>f(x)</em> = 7/(1<em> </em>+ <em>x</em>), then
<em>f</em> (2) = 7/3
<em>f '(x)</em> = -7/(<em>x</em> + 1)² ==> <em>f '</em> (2) = -7/9
<em>f ''(x)</em> = 14/(<em>x</em> + 1)³ ==> <em>f ''</em> (2) = 14/27
<em>f '''(x)</em> = -42/(<em>x</em> + 1)⁴ ==> <em>f '''</em> (2) = -14/27
Then the Taylor series of <em>f(x)</em> about <em>a</em> = 2 is
7/3 + 1/1! (-7/9) (<em>x</em> - 2) + 1/2! (14/27) (<em>x</em> - 2)² + 1/3! (-14/27) (<em>x</em> - 2)³
= 7/3 - 7/9 (<em>x</em> - 2) + 7/27 (<em>x</em> - 2)² - 7/81 (<em>x</em> - 2)³
