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Scientists modeled the intensity of the sun, I, as a function of the number of hours since 6:00 a.m., h, using the

12h-h?

function I(h)= They then model the temperature of the soil, T, as a function of the intensity using the

36

function T ( 1) = 150007. What is the temperature of the soil at 2:00 p.m., to the nearest whole number?

Sagot :

MrRoyalidn

The functions are illustrations of composite functions.

The soil temperature at 2:00pm is 67

The given parameters are:

[tex]\mathbf{I(h) =\frac{12h - h^2}{36}}[/tex] ---- the function for sun intensity

[tex]\mathbf{T(I) =\sqrt{5000I}}[/tex] -- the function for temperature

At 2:00pm, the value of h (number of hours) is:

[tex]\mathbf{h = 2:00pm - 6:00am}[/tex]

[tex]\mathbf{h = 8}[/tex]

Substitute 8 for h in [tex]\mathbf{I(h) =\frac{12h - h^2}{36}}[/tex], to calculate the sun intensity

[tex]\mathbf{I(8) =\frac{12 \times 8 - 8^2}{36}}[/tex]

[tex]\mathbf{I(8) =\frac{32}{36}}[/tex]

[tex]\mathbf{I(8) =\frac{8}{9}}[/tex]

Substitute 8/9 for I in [tex]\mathbf{T(I) =\sqrt{5000I}}[/tex], to calculate the temperature of the soil

[tex]\mathbf{T(8/9) =\sqrt{5000 \times 8/9}}[/tex]

[tex]\mathbf{T(8/9) =\sqrt{4444.44}}[/tex]

[tex]\mathbf{T(8/9) =66.67}[/tex]

Approximate

[tex]\mathbf{T(8/9) =67}[/tex]

Hence, the soil temperature at 2:00pm is 67

Read more about composite functions at:

https://brainly.com/question/20379727

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