Question 7 of 14 Sapling Learning Consider the following expression. 6.90 x 10 x

Question

Question 7 of 14 Sapling Learning Consider the following expression. 6.90 x 10 x (0.100+x 1 We can solve for x using a technique called successive approximations. Step 1: If we assume that xis very small compared to 0.100 (suchthat 0.100 x 0.100) then our first approximation of x (let's it x) can be calculated as 6.90 x 10 o.100) Number Express all answers to three or more significant figures. Step 2: Now, take your first approximation of x and plug it into the full equation. 6.90 x 10 x, (0.100+x) Number Step 3: Each successive approximation uses the value from the previous approximation. 6.90 x 10 r (0.100 r 12 O Previous ® Give up & View solution Check Answer 0 Next HExt Hint

Explanation / Answer

step 1

6.9*10^-5    = x1(0.1)^2

x1 = 0.0069

step2

6.9*10^-5    = x2(0.1+x1)^2

6.9*10^-5    = x2(0.1+0.0069)^2

x2 = 0.0060

step3

6.9*10^-5    = x3(0.1+x2)^2

6.9*10^-5    = x3(0.1+0.006)^2

   x3            = 0.00614

step4

6.9*10^-5    = x4(0.1+x3)^2

6.9*10^-5    = x4(0.1+0.00614)^2

        x4        = 0.00612

step4

6.9*10^-5    = x5(0.1+x4)^2

6.9*10^-5    = x5(0.1+0.00612)^2

x5            = 0.00613

x4 and x5 are three significant figures

x1 and x2 are two significant figures

     

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