How does changing the scale change the distance represented?

Mathematics

1 answer:

gavmur [86]3 years ago

8 0

No changing the map scale does not change actual distances.

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when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four s

Eva8 [605]

Answer:

The stone would take approximately 10.107 seconds to fall 500 meters.

Step-by-step explanation:

According to the statement of the problem, the following relationship of direct proportionality is built:

$t \propto y^{1/2}$

$t = k\cdot t^{1/2}$

Where:

$t$ - Time spent by the stone, measured in seconds.

$y$ - Height change experimented by the stone, measured in meters.

$k$ - Proportionality constant, measured in $\frac{s}{m^{1/2}}$ .

First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

$k = \frac{t}{y^{1/2}}$

If $t = 4\,s$ and $y=78.4\,m$ , then:

$k = \frac{4\,s}{(78.4\,m)^{1/2}}$

$k \approx 0.452\,\frac{s}{m^{1/2}}$

Then, the expression is $t = 0.452\cdot y^{1/2}$ . Finally, if $y = 500\,m$ , then the time is:

$t = 0.452\cdot (500\,m)^{1/2}$

$t \approx 10.107\,s$

The stone would take approximately 10.107 seconds to fall 500 meters.

4 0

3 years ago

A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers

icang [17]

Answer:

$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$