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3 years ago

Simplify the expression with using scientific notation (4 times 10 8)2

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

The scientific notation:

$a\cdot10^n\\\\1\leq a < 10;\ n\in\mathbb{Z}$

$(4\cdot10^8)^2=4^2(10^8)^2=16\cdot10^{8\cdot2}=16\cdot10^{16}\\\\=1.6\cdot10\cdot10^{16}=1.6\cdot10^{17}$

Used:

$(a\cdot b)^n=a^n\cdot b^n\\\\(a^n)^m=a^{n\cdot m}\\\\a^n\cdot a=a^{n+1}$

Answer: (4 × 10⁸)² = 1.6 × 10¹⁷

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a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3>Solution:</h3>

a. The points (-4,1) and (2,4) both lie on the line

The general line equation on which (a, b) and (c, d) lies is:

$y-\mathrm{b}=\frac{d-b}{c-a}(x - a)$

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

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On solving we get,

$\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}$

b.) m= -1 and the point (2, -1) lies on the line

The equation of line in point slope form is y – b = m(x – a)

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)

y + 1 = -x + 2

y = -x + 2 -1

y = -x + 1

c. )It has the same slope as y = 5 and passes through (1, 1)

our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1

Then our equation will be y = k

y = 1

d. ) m= -3 and it has a y-intercept of (0, 8)

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

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