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3 years ago

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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What is 5 raised to the 5th power?

Roman55 [17]

Five raised to the fifth power 5^5 5*5*5*5*5 = 3,125

8 0

3 years ago

Read 2 more answers

Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

6 0

3 years ago

During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the rem

Lelechka [254]

Answer:

200 kg

Step-by-step explanation:

First hour he sold 15% (remaining is 85%)

Second hour he sold 20% of remaining (which is 85%) -- so he sold $(0.2)(0.85)=0.17$ , which is 17% (remaining 85-17=68%)

Third hour he sold 25% of remaining (which is 68%) -- so he sold $(0.25)(0.68)=17$ , which is 17%

In third hour he sold 34, so 17% is 34. To find total he initially had, we need to find (100%). We can setup the ratio (letting x equal his initial amount):

$\frac{0.17}{34}=\frac{1}{x}\\0.17x=34\\x=\frac{34}{0.17}=200$