An unevenly heated plate has temperature T(x, y) in °C at the point (x, y). If T(2, 1) = 130, and Tx(2, 1) = 16, and Ty(2, 1) = −13, estimate the temperature at the point (2.03, 0.96). (Round your answer to 2 decimal places.)

The estimated temperature at the point (2.03, 0.96) is 131

Step-by-step explanation:

In this question, we are to estimate the temperature at the given point using the temperature of the unevenly heated plate.

We proceed as follows;

In the question, we identify that the temperature at the point T(2,1) = 130 degrees celcius

Now, let’s look at how the temperature changes. There is a positive change of 16 units when we move across the x-axis and a negative decrease when we move up the y-axis to a tune of 16 units(negative)

Now, how does the problem wants us to move using the notation of change?

Look at the point (2.03, 0.96), since movement across the x-axis is positive, the motion here in terms of x i.e Δx is 0.03 while the corresponding motion in terms of y(albeit negative) is Δy = -0.04

Mathematically, the change in temperature is proportional to the distance traveled. What this means is that we need to multiply the changes in direction by the corresponding temperature. This is shown below;

ΔTx =Δx*Tx(2,1) => ΔTx = (0.03)*(16) = 0.48

ΔTy = Δy*Ty(2,1) => ΔTy = (-0.04)*(-13) = 0.52

We can now combine the equations above to form a single one as follows; which is an approximation;

ΔT = Δx*Tx(2,1) + Δy*Ty(2,1) => ΔT = (0.03)*(16) + (-0.04)*(-13) = 1

To arrive at the final answer, we add the change in temperature to the staring temperature which is ;

T(2.03,0.96) = T(2,1) + ΔT = 130 + 1= 131

250

step-by-step explanation:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.