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Kamila [148]
4 years ago
6

How do I approximate a square root

Mathematics
1 answer:
Roman55 [17]4 years ago
4 0
The calculus approach is to use Newtons Method:
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
where 
f(x) = x^2 - a
Start with initial guess of "a".
After 4 or 5 iterations, you should get a close approximation to \sqrt{a}
...............

If you wanted a non-calculus approach, I would suggest divide and conquer.
First determine which 2 integers the sqrt lies in between by perfect squares.
m^2\ \textless \ a \ \textless \ n^2
Then use midpoint \frac{m+n}{2} for next guess, if 
(\frac{m+n}{2})^2 \ \textless \  a
then repeat with "m" = midpoint. Otherwise repeat with "n" = midpoint.
Continue until you have a good approximation, about 6-8 decimal points.
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How many pounds are in 9 gallons?​
pishuonlain [190]

Answer: 75.108

Step-by-step explanation:

1 gallon is 8.3454 lb so multiply by 9 to get the answer

8.345*9= 75.105 lbs

So there are 75 lbs in 9 gallons

8 0
3 years ago
5. A dinner bill of $31.37 had 6% tax added to that total. What was the amount of the tax?
stellarik [79]
$31.37 multipled by 6% (or 0.006)= $1.88 in tax.

The total amount for the dinner bill would be $33.25 including tax.
3 0
3 years ago
In a linear equation relating income and consumption, you know that the intercept is $1,000 and the slope of the line is 4. if i
Amiraneli [1.4K]
A general equation of a linear function is expressed as y = mx + b where m represents the slope and b is the y-intercept. The slope is the rate of change of y with respect x which is equal to 4 for this problem. The y-intercept represents the value when x is equal to zero. It is the initial value of y. In this case, it is equal to $1,000. The linear equation would be:

y = 4x + 1000

assuming y is the income and x is the consumption.

At an income (y) equal to $20,000, we can calculate for the consumption.

20000 = 4x + 1000
19000 = 4x
x = 4750
3 0
3 years ago
Which shows how to find the value of this expression when x=-2 and y=5? (3x^3y^-2)^2
yanalaym [24]

Answer:

1st one

Step-by-step explanation:

I have answered ur question

3 0
3 years ago
An acute angle θ is in a right triangle with cos θ = 9/10 . What is the value of sec θ?
xenn [34]

By definition

... sec(θ) = 1/cos(θ) . . . . trig identity

... sec(θ) = 1/(9/10) . . . . substitute the given value, then simplify to ...

... sec(θ) = 10/9

8 0
3 years ago
Read 2 more answers
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