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gulaghasi [49]
3 years ago
15

Explain algebraically using properties of logs how log(100x) is related to log(x)

Mathematics
1 answer:
DIA [1.3K]3 years ago
4 0
Log(100x)=log(100)+logx
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Light travels at a rate of 3.0 x 108 meters per second. If the earth is 1.5 x 1011 meters away from the sun, how long does it ta
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I am assuming you mean 3.0 *10^8 and 1.5 * 10^11.

time = distance/speed right. So, 
t = 500 s

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How many different 13 card bridge hands can be selected from an ordinary deck?
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Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or a
White raven [17]
Check the picture below

now, we know is a parallelogram, so the diagonals will bisect

looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason

is it a rhombus?  well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal

now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal

\bf \textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%  (a,b)&#10;J&({{-7 }}\quad ,&{{ -2}})\quad &#10;%  (c,d)&#10;K&({{ 0}}\quad ,&{{ 4}})\\\\&#10;K&({{ 0}}\quad ,&{{ 4}})\quad &#10;%  (c,d)&#10;L&({{ 9}}\quad ,&{{ 2}})&#10;\end{array}\qquad &#10;%  distance value&#10;d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}&#10;\\\\\\&#10;JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2}&#10;\\\\\\&#10;JK=\sqrt{7^2+6^2}&#10;\\\\\\&#10;KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}

now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL

and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1

\bf \begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%   (a,b)&#10;K&({{ 0}}\quad ,&{{ 4}})\quad &#10;%   (c,d)&#10;M&({{ 2}}\quad ,&{{ -4}})&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope = {{ m}}= \cfrac{rise}{run} \implies &#10;\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-4}{2-0}

\bf -------------------------------\\\\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%   (a,b)&#10;J&({{ -7}}\quad ,&{{ -2}})\quad &#10;%   (c,d)&#10;L&({{ 9}}\quad ,&{{ 2}})&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope = {{ m}}= \cfrac{rise}{run} \implies &#10;\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-(-2)}{9-(-7)}\implies \cfrac{2+2}{9+7}

then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.

7 0
3 years ago
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Find the volume of each square pyramid given its slant height. Round to the nearest tenth. It looks like a normal pyramid with a
Luden [163]

Answer:

1.344 cubic units

Step-by-step explanation:

Given data

Base edge a= 1.2

Hieght= 2.8

The expression for the volume of a pyramid is

V= a^2h/3

substitute

V= 1.2^2* 2.8/3

V= 1.44*2.8/3

V= 4.032/3

V= 1.34cubic units

5 0
2 years ago
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