In the vicinity of a bonfire the temperature t (in °c) at a distance of x meters from the center of the fire is given by t(x)=500000/(x^2+400). At what range distances from the fire's center is the temperature less than 210°c?

[tex]t(x)<210\\\\\dfrac{500000}{x^2+400}<210\\\\\dfrac{500000}{210}<x^2+400 \quad\text{multiply by $(x^2+400)/210$}\\\\1980.95<x^2 \quad\text{subtract 400}\\\\44.508<x[/tex]

At distances greater than 44.51 meters, the temperature is less than 210 °C.

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codiepienagoya codiepienagoya · Answer 2 · 2021-09-26T22:53:18+02:00

The neighborhood is indeed the region as well as the nearest stuff. These same four blocks around a building and all the stores and items in that four-block range are examples from the immediate area, and the further calculation can be defined as follows:

Given:

[tex]\bold{t(x)=\frac{500000}{(x^2+400)}}[/tex]

[tex]\text{temperature} < 210^{\circ} \ C[/tex]

Calculating the x value:

[tex]\to \bold{t(x)=210}\\\\\to \bold{\frac{500000}{(x^2+400)}=200} \\\\\to \bold{\frac{500000}{210}= (x^2+400)}\\\\\to \bold{\frac{50000}{21}= (x^2+400)}\\\\\to \bold{2380.95= (x^2+400)}\\\\\to \bold{1980.95= x^2}\\\\\to \bold{x=\sqrt{1980.95} }\\\\\to \bold{x=44.50 }\\\\[/tex]

Temperature is less than 210°C at distances of more than 44.51 meters.

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