Question

Determine if the outside temperature is a function of the time of day or if the time of day is a function of temperature

Answer 1

Answer:

Temperature is a function of the time of the day.

Step-by-step explanation:

Temperature is a function of the time of the day.

Like if we see the function $f(x)=y$ , we can see that y is dependent on the value of x.

So, the temperature outside is generally dependent upon the time if day.

The time of the day is not dependent on the temperature. The time goes as it is, irrespective of the temperature.

Answer 2

The polynomial of order three equation is given as $\rm T(^oC)= \dfrac{5}{21}t^3 -\dfrac{709}{140} t^2+ \dfrac{13439}{420} t+ \dfrac{286}{7}$.

a.  For t = 11, T(°C) = 96.96.

b.  For t = 8, T(°C) = 94.63.

c.  T(°C) = -219.95

What is polynomial?

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

We know the cubic polynomial is given by ax³ + bx² + cx + d.

Then the function will be

T(°C) = at³ + bt² + ct + d

At t = 2, T(°C) will be 86.5, then the equation will be

8a + 4b + 2c + d = 86.5 ...(i)

At t = 3, T(°C) will be 97.7, then the equation will be

27a + 9b + 3c + d = 97.7 ...(ii)

At t = 5, T(°C) will be 104, then the equation will be

125a + 25b + 5c + d = 104 ...(iii)

At t = 10, T(°C) will be 92.5, then the equation will be

1000a + 100b + 10c + d = 92.5 ...(iv)

On solving the equations (i), (ii), (iii), and (iv), we have

$\rm a = \dfrac{5}{21}\\\\\\b = \dfrac{-709}{140}\\\\\\c = \dfrac{13439}{420}\\\\\\d = \dfrac{286}{7}$

Then the polynomial equation will be.

$\rm T(^oC)= \dfrac{5}{21}t^3 -\dfrac{709}{140} t^2+ \dfrac{13439}{420} t+ \dfrac{286}{7}$

a)  For t = 11, the temperature will be

T(°C) = 96.96

b)  For t = 8, the temperature will be

T(°C) = 94.63

c) If second order is used instead of the third order, we have the equation

$\rm T(^oC)= -\dfrac{709}{140} t^2+ \dfrac{13439}{420} t+ \dfrac{286}{7}$

At x = 11, the temperature will be

T(°C) = -219.95

More about the polynomial link is given below.

https://brainly.com/question/17822016