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Kitty [74]
3 years ago
11

Explain how you can approximate a cube root when the cube is not a perfect cube.

Mathematics
2 answers:
jenyasd209 [6]3 years ago
5 0

Answer:

See below.

Step-by-step explanation:

It would take a long time to explain . There is a good method called Newton's method which involves graphs of the type

y = x^3 - n and applying calculus to produce cycles of approximation  until you'll get close to the required cubic root.

You'll find it on online videos.

bagirrra123 [75]3 years ago
3 0

Step-by-step answer:

You can  use Newton's method as follows:

It is an iterative method, meaning that from an approximation (i.e. an approximate solution), we can refine the answer to get a closer approximation.  By repeating the process (iteration), we can get an answer as accurate as we wish.

The basis of the formula is based on

x1=x0-f(x0)/f'(x0)

where

x0 is a given approximation

x1 is a better approximation

f(x) is a given function (for which we need the roots)

f'(x) is the derivative of the function.

Skipping all details and applying directly to find the cube root, we have

N=the number for which the cube root is desired

f(x)=x^3-N

f'(x)=3x^2

and x0 is an initial approximation that we need to provide (from the integer cubes, for example).

Say we need to find the cube-root of 124.

We know that 5^3 = 125, a rather close approximation, but the cube root is slightly less than 5.

To find a better approximation, we apply Newton's method, and calculate mentally:

x0=5, N=124

x1 = x0-(x0^3-124)/(3(x0^2))    [next substitute values]

= 5 - (125-124)/(3(5^2))     [ next simplify ]

= 5-1/75    [next, rearrange to calculate mentally ]

=5-(1/25)/3  [ next, substitute 1/25 = 0.04, 1/3 division can be done mentally ]

= 5 - 0.04/3    [ divide 0.04/3 mentally ]

= 5 - 0.013333    [ subtract ]

= 4.98667

(exact value = 4.98663, first approximation is already quite close)

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suter [353]

Answer:

0.67

Step-by-step explanation:

Formula: k = y/x

k = 2/3

k = 0.66666666666

k = 4/6

k= 0.66666666666

k = 6/9

k = 0.66666666666

k = 8/12

Round 0.67

Hence, answer = 0.67

[RevyBreeze]

8 0
2 years ago
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blagie [28]
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3 years ago
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Two 120 resistors are connected in parallel across voltage supply of 10 vdc what’s the current in this circuit
Daniel [21]

Answer: 0.167

Step-by-step explanation:

This is an applied mathematics question

Resistors in parallel  ⁾/R = ¹/₁₂₀ + ¹/₁₂₀ since the resistor is two 120

Therefore , resolve into fraction now yield

                       ¹/R                              =         1 + 1  

                                                                    -------

                                                                     120

                                                          =         2/120

                                                          =          ¹/₆₀

Therefore,                                  ¹/R   =      ¹/₆₀

 Cross multiply to get R the resistance

                                                      R  =  60

From formula,                                V = IR where I is the current

There fore making I the subject of the formula

                                                        I = V/R

                                                          = 10/60

                                                          = 0.166

                                                          = 0.167 A, A = ampere which is the unit of current.

                   

4 0
3 years ago
How would I solve this? Can I get steps?
ratelena [41]

Answer:

<em>p = ± q / 5r + 8; Option D</em>

Step-by-step explanation:

We are given the following equation; q^2 / p^2 - 16p + 64 = 25r^2;

q^2 / p^2 - 16p + 64 = 25r^2 ⇒ Let us factor p^2 - 16p + 64, as such,

p^2 - 16p + 64,

( p )^2 - 2 * ( p ) * ( 8 ) + ( 8 )^2,

( p - 8 )^2 ⇒ Now let us substitute this into the equation q^2 / p^2 - 16p + 64 = 25r^2 in replacement of p^2 - 16p + 64,

q^2 / ( p - 8 )^2 = 25r^2 ⇒ multiply either side by ( p - 8 )^2,

q^2 = 25r^2 * ( ( p - 8 )^2 ) ⇒ divide either side by 25r^2,

q^2 / 25r^2 = ( p - 8 )^2 ⇒ Now apply square root on either side,

| p - 8 | = √( q^2 / 25r^2 ) ⇒ Simplify,

| p - 8 | = q / 5r,

| p | = q / 5r + 8,

<em>Answer; p = ± q / 5r + 8; Option D</em>

8 0
2 years ago
Help with calculus please?
Kazeer [188]
Wait let me know that the .12 means in the first question and i will fix the answer

int (x)(cosx) dx 

u=x      ----> take derivative     du=dx
dv=cosx    -----> take integral  v=sinx

now use integration by parts 

u v - int (v)du
x sinx - int (sinx) (1) dx=

x sinx  - (-cos(x)) + c =

answer is = x sinx + cosx + c



3 0
2 years ago
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