Answer:
A. x = 11/16
Step-by-step explanation:
For the purpose here, it is convenient to rearrange the equation to f(x) -g(x) = 0. We know the root will be in the interval [0, 1] because (f-g)(0) = -3 and (f-g)(1) = +3. At each iteration, we evaluate (f-g)(x) at the midpoint of the interval to see which of the interval end points can be moved and still bracket the root.
Using the bisection method starting with the interval [0, 1] we find f(1/2)-g(1/2) < 0, so we can move the interval limits to [1/2, 1].
For the next iteration, we find f(3/4) -g(3/4) > 0, so we can move the interval limits to [1/2, 3/4].
For the third iteration, we find f(5/8) -g(5/8) < 0, so we can move the interval limits to [5/8, 3/4].
Then the root is approximately the middle of that interval:
x ≈ (5/8 +3/4)/2 = 11/16
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This value of x is 0.6875. The root is closer to 0.639802004233. The bisection method takes about 3 iterations for each decimal place of accuracy. Other methods can nearly double the number of accurate decimal places on each iteration.
Answer:
0
Step-by-step explanation:
slope m = (y₂ - y₁) / (x₂ - x₁)
= (5 - 5) / (4 - 9)
= 0 / -5
= 0
Answer:
For given linear equation having infinite many solution the value of k is 20 .
Step-by-step explanation:
Given as :
The equation is 2 (4 x + 10) = 8 x + k
For infinite many solution , if the variable cancel out to zero then it will have infinite many solutions
<u>So, from given linear equation</u>
i.e 2 (4 x + 10) = 8 x + k
Or, 2 × 4 x + 2 × 10 = 8 x + k
Or, 8 x + 2 × 10 = 8 x + k
Or, 8 x + 20 = 8 x + k
Or, k + (8 x - 8 x) = 20
Or, k + 0 = 20
∴ k = 20
So, The vale of k = 20
Hence, For given linear equation having infinite many solution the value of k is 20 . Answer
Answer:
c = 1.29s + 2
Step-by-step explanation:
c represents the total cost
s represents the number of songs downloaded
1.29 represents the cost charged for every song downloaded
2 represents the initial cost to download the app
Answer:
Step-by-step explanation:
hello :
cot x + 2cot x sin x = 0 0≤ x≤ 180
cotx(1+2sinx) =0 means : cotx=0 or 1+2sinx=0
1) cotx=0 so : cosx=0 and sinx ≠ 0 because cotx = cosx/sinx
when : 0≤ x≤ 180 : x=90°
2) 1+2sinx=0 means : sinx = -1/2
when : 0≤ x≤ 180 : no solutions because : sinx ≥ 0
conclusion : one solution : x=90°
