Express the following numbers in scientific notation. (a) 2 000 000 000 000 000 000 000 000 m

(b) 0.000 000 000 000 000 000 151 m

(c) 5 036 000 000 m

(d) 0.000 000 105 0 m

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Ответ:

rodrickahammonds

15.06.2022

Mathematics

$x = \dfrac{110}{31}; \qquad y = \dfrac{72 }{31}$

Step-by-step explanation:

I am guessing that your two equations are

(1) ⅕x + ⅛y = 1

(2) ½x - ⅓ y = 1

To get rid of fractions, I would multiply each equation by the least common multiple of its denominators.

$\begin{array}{rcrl}(3) \qquad 8x + 5y & = & 40 & \text{Multiplied (1) by 40}\\(4) \qquad 3x - 2y & = & 6 & \text{Multiplied (2) by 6}\\\end{array}$

We can solve this system of equations by the method of elimination.

$\begin{array}{rcrl}(5) \qquad \, \, 16x + 10y & = & 80 & \text{Multiplied (3) by 2}\\(6) \qquad \, \: 15x - 10 y & = & 30 & \text{Multiplied (4) by 5}\\31x & = & 110 & \text{Added (5) and (6)}\\\\(7)\qquad\qquad \qquad x & = & \dfrac{110 }{31} & \text{Divided each side by 31}\\\end{array}$

$\begin{array}{rcrl}3 \left (\dfrac{110}{31} \right) - 2y & = & 6 & \text{Substituted (7) into (4)}\\\\ (5) \qquad16x + 10y & = & 80 & \text{Multiplied (3) by 2}\\\\(6)\qquad 15x - 10 y & = & 30 & \text{Multiplied (4) by 5}\\\\31x & = & 110 & \text{Added (5) and (6)}\\\\(7)\qquad \qquad \qquad x & = & \dfrac{110 }{31} & \text{Divided each side by 31}\\\\3 \left(\dfrac{110}{31} \right ) - 2y & = & 6 & \text{Substituted (7) into (4)}\\\\\end{array}\\\\$

$\begin{array}{rcll}\dfrac{330}{31} - 2y & = & 6 &\\\\-2y & = & 6 - \dfrac{330}{31} &\\\\y & = & \dfrac{165}{31} -3 & \text{Divided each side by -2}\\\\ & = & \dfrac{165 - 93}{31} &\\\\ & = & \dfrac{72}{31} &\\\\\end{array}\\\\\therefore x = \dfrac{110}{31}; \qquad y = \dfrac{72 }{31}$

The diagram below shows the graphs of your two functions intersecting at (3.548, 2.323). These are the decimal equivalents of your fractional coordinates.

Of : 1/5 x + 1/8 y = 1 1/2 x − 1/3 y = 1

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Express the following numbers in scientific notation. (a) 2 000 000 000 000 000 000 000 000 m (b) 0.000 000 000 000 000 000 151 m (c) 5 036 000 000 m (d) 0.000 000 105 0 m