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Novosadov [1.4K]
3 years ago
10

Which of the numbers, 3/12 or 2/9, is greater? How do you know?

Mathematics
1 answer:
nata0808 [166]3 years ago
7 0

Answer:

3/12 > 2/9

Step-by-step explanation:

Well, 3/12 in decimal form is 0.25, and 2/9 in decimal form is around 0.23 so that would make 3/12 the greater fraction.

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Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=
luda_lava [24]

Let f(x) = x^3 - 2x - 2. Then differentiating, we get

f'(x) = 3x^2 - 2

We approximate f(x) at x_1=2 with the tangent line,

f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18

The x-intercept for this approximation will be our next approximation for the root,

10x - 18 = 0 \implies x_2 = \dfrac95

Repeat this process. Approximate f(x) at x_2 = \frac95.

f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}

Then

\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}

Once more. Approximate f(x) at x_3.

f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}

Then

\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}

Compare this to the actual root of f(x), which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

4 0
2 years ago
Solve for x solve for x ​
zhenek [66]

Answer:

9

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
ILL GIVE BRAINLEST ​
Lerok [7]

Answer:

its the first one brsinlest plz

Step-by-step explanation:

3 0
3 years ago
A set of data may have more than one mode.<br> (1 Point)<br> True<br> False
JulsSmile [24]
True

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6 0
3 years ago
PLEASE INCLUDE ALL STEPS! BRAINLIEST GETS 25+ POINTS!!
lora16 [44]

Answer:

Roberto did 4 or 5 hours

Step-by-step explanation:

r- Roberto

e- Edward

j- Jim

j = 1 hr. paddled

r= 2e for the number of hours, r, robert paddled.

r+ e+ j < 10 Substitute in for r and j.

2e+ e+ 1 < 10

3e <9

e< 3

r = 2*e

r < 2*3  I Changed it to less than, so because edward has to do less than 3 hours, so now im finding the number of hours that he has to be below.

r<6

Roberto did less than 6 hours.  

Edward did less than 3 hours.

Jim did 1 hour.

Possible Combination of hours that satisfies all the criteria and is below 10 total hours:

Jim Does 1 hour, Edward does 2 hours, and Roberto does 4  hours.

Another Possibility is

Jim does 1 hours, Edward does 2.5 hours and Roberto does 5 hours.

(Edward has to do 2.5 hours for Roberto to do 5 hours, because it states that Roberto does twice as many hours as Edward, it does not state that he did more than twice as many hours so it is necessary for Edward to do 2.5 hours for Roberto to do 5.)

4 0
3 years ago
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