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The distances between some planets are given below.


Planet Q is 3.6 x 10 to the power of 6 km from planet P.

Planet R is 1.6 x 10 to the power of 7 km from planet P.


Work out the shortest distance between

planet Q and planet R.

Give your answer in standard form.

Sagot :

MrRoyalidn

The shortest distance between  planet Q and planet R is [tex]1.64 \times 10^7\ km[/tex]

Distance

The distance between points is the number of units between them

The distances between some planets are given as:

[tex]QP = 3.6 \times 10^6[/tex]

[tex]RP = 1.6 \times 10^7[/tex]

Shortest distance

The shortest distance (x) is then calculated using the following Pythagoras theorem

[tex]x^2 = RP^2 + QP^2[/tex]

This gives

[tex]x^2 = (3.6 \times 10^6)^2 + (1.6 \times 10^7)^2[/tex]

Evaluate the squares

[tex]x^2 = 12.96 \times 10^{12} + 2.56 \times 10^{14}[/tex]

Rewrite as:

[tex]x^2 = 12.96 \times 10^{12} + 256 \times 10^{12}[/tex]

Evaluate the sums

[tex]x^2 = 268.96\times 10^{12}[/tex]

Take square roots of both sides

[tex]x = 16.4\times 10^{6}[/tex]

Rewrite as:

[tex]x = 1.64\times 10^{7}[/tex]

Hence, the shortest distance between  planet Q and planet R is [tex]1.64 \times 10^7\ km[/tex]

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