A) La distancia del Sol a Neptuno en notación científica es 45 x 10^8 km.
B) Júpiter se encuentra a 930.000.000 kilómetros del Sol.
C) La distancia del Sol a Neptuno es 30 veces mayor que la que hay a la Tierra.
Dado que la distancia entre la tierra y el sol es de 1,5 . 10˄8 km, la distancia entre la Tierra y Júpiter es de 9,3 . 10˄8 km y Neptuno está situado a 4.500.000.000 Km del Sol, para determinar:
A) Expresa en notación científica la distancia del sol a Neptuno
B) Calcula la distancia a la que está situado Júpiter respecto al Sol
C) Calcula cuantas veces es mayor la distancia del Sol a Neptuno que la que hay a la Tierra.
Deben realizarse los siguientes cálculos:
- A) 4.500.000.000 = 45 x 100.000.000
- 100.000.000 = 10^8
- 4.500.000 = 45 x 10^8
- B) 9.3 x 10^8 = X
- 100.000.000 = 10^8
- 9.3 x 100.000.000 = X
- 930.000.000 = X
-
C) Tierra = 150.000.000
- Neptuno = 4.500.000.000
- 150 = 1
- 4.500 = X
- 4500 / 150 = X
- 30 = X
Aprende más en brainly.com/question/1705769
Answer:
Hi There!
Your answer is:
<u>Length = 116</u>
<u>Width = 56</u>
Step-by-step explanation:
L= 4+ 2w
Width=w
perimeter formula
l+l+w+w= perimeter
Subsitute L for 4+2w
(4+2w)+(4+2w) + (w) + (w) = 344
8 +4w+w+w = 344
8+ 6w = 344
-8
6w = 336
/6
w= 56
PLUG BACK IN!
Length = 4+ 2w
Length = 4+ 2(56)
<u>Length = 116</u>
<u>Width = 56</u>
CHECK YOUR WORK
116+116+56+56= 344???
344 = 344 YES
HOPE THIS HELPS
Answer: 5 1/2 hours OR 5 hrs 30 minutes
Step-by-step explanation:
She travels for 8 hours
Out of this, 2 1/2 hours she takes a break.
She has actually travelled 5 1/2 hours
Answer:
62
Step-by-step explanation:
we have given ![a> 2](https://tex.z-dn.net/?f=a%3E%202)
then ![\frac{2}{a}\ ,\frac{3}{a+1}\ ,\frac{4}{a+2}\ , \frac{5}{a+3}\ ,\frac{6}{a+4}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Ba%7D%5C%20%2C%5Cfrac%7B3%7D%7Ba%2B1%7D%5C%20%2C%5Cfrac%7B4%7D%7Ba%2B2%7D%5C%20%2C%20%5Cfrac%7B5%7D%7Ba%2B3%7D%5C%20%2C%5Cfrac%7B6%7D%7Ba%2B4%7D)
since it is given that ![a> 2](https://tex.z-dn.net/?f=a%3E%202)
so
![a\equiv 2\ mod\ 6](https://tex.z-dn.net/?f=a%5Cequiv%202%5C%20mod%5C%206)
![a\equiv2 \left ( mod\ 2,3,4,5,6 \right )](https://tex.z-dn.net/?f=a%5Cequiv2%20%5Cleft%20%28%20mod%5C%202%2C3%2C4%2C5%2C6%20%5Cright%20%29)
![a\equiv2 \left ( mod\ lcm\left ( 2,3,4,5,6 \right )\right )](https://tex.z-dn.net/?f=a%5Cequiv2%20%5Cleft%20%28%20mod%5C%20lcm%5Cleft%20%28%202%2C3%2C4%2C5%2C6%20%5Cright%20%29%5Cright%20%29)
![a\equiv2 \left ( mod\ 60 \right )](https://tex.z-dn.net/?f=a%5Cequiv2%20%5Cleft%20%28%20mod%5C%2060%20%5Cright%20%29)
then a=60n+2 where n is a positive integer
so smallest value of a is a=60×1+2=62
Step-by-step explanation:
<h3>Appropriate Question :-</h3>
Find the limit
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
![\large\underline{\sf{Solution-}}](https://tex.z-dn.net/?f=%5Clarge%5Cunderline%7B%5Csf%7BSolution-%7D%7D)
Given expression is
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
On substituting directly x = 1, we get,
![\rm \: = \: \sf \dfrac{1-2}{1 - 1}-\dfrac{1}{1 - 3 + 2}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%5Cdfrac%7B1-2%7D%7B1%20-%201%7D-%5Cdfrac%7B1%7D%7B1%20-%203%20%2B%202%7D)
![\rm \: = \sf \: \: - \infty \: - \: \infty](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5Csf%20%5C%3A%20%5C%3A%20-%20%5Cinfty%20%5C%3A%20-%20%5C%3A%20%5Cinfty%20)
which is indeterminant form.
Consider again,
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
can be rewritten as
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%203x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%202x%20-%20x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20x%28x%20-%202%29%20-%201%28x%20-%202%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%7B%28x%20-%202%29%7D%5E%7B2%7D%20-%201%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%202%20-%201%29%28x%20-%202%20%2B%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%28x%20-%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%7D%7Bx%28x%20-%202%29%7D%5Cright%5D)
![\rm \: = \: \sf \: \dfrac{1 - 3}{1 \times (1 - 2)}](https://tex.z-dn.net/?f=%20%20%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%5C%3A%20%5Cdfrac%7B1%20-%203%7D%7B1%20%5Ctimes%20%281%20-%202%29%7D%20)
![\rm \: = \: \sf \: \dfrac{ - 2}{ - 1}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%5C%3A%20%5Cdfrac%7B%20-%202%7D%7B%20-%201%7D%20)
![\rm \: = \: \sf \boxed{2}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%5Cboxed%7B2%7D%20)
Hence,
![\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}](https://tex.z-dn.net/?f=%5Crm%5Cimplies%20%5C%3A%5Cboxed%7B%20%5Crm%7B%20%5C%3A%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D%20%3D%202%20%5C%3A%20%7D%7D)
![\rule{190pt}{2pt}](https://tex.z-dn.net/?f=%5Crule%7B190pt%7D%7B2pt%7D)