The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y,...

The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee is constrained to live on a sphere of radius 3 centered at the origin. In other words, the bee cannot fly off of this sphere. What is the coldest temperature that the bee can experience on this sphere? Where does this occur? What is the hottest temperature that the bee can experience on this sphere? Where does this occur?

Expert Solution

Colby Messinger answered 2 years ago

The temperature T at (x,y,z) in the 3D space is given by T(x,y,z) = ln(1+x2y2+z2). a)...

The temperature T at (x,y,z) in the 3D space is given by T(x,y,z) = ln(1+x2y2+z2). a) Find rate of change of T at the point P(1,-1,-1) in the direction of Q(2,0,0)? b) In which direction from P(1,-1,-1) does the temperature T increase most rapidly? c) What is the maximum rate of change of T at P(1,-1,-1)?

The temperature X in degrees Fahrenheit (F) of a particular chemical reaction is known to be...

The temperature X in degrees Fahrenheit (F) of a particular chemical reaction is known to be distributed between 220 and 280 degrees with a probability density function of fX(x) = (x − 190)/3600. A value of X degrees Fahrenheit can be converted to Y degrees Celsius (C) by taking Y = (5/9)(X − 32). Determine the following in both degrees F and degrees C: (a) the mean of the distribution (b) the variance of the distribution (c) the cumulative distribution...

The high temperature (in degrees Fahrenheit), x, and the ice cream sales (in dollars) for a...

The high temperature (in degrees Fahrenheit), x, and the ice cream sales (in dollars) for a local store, y, are related by the regression line equation y = -392.966 + 8.791x. Find the amount of sales predicted by the model if the high temperature is x = 94°F. Give your answer as a monetary amount rounded to the nearest cent.

The temperature T at a point (x,y,z) in space is inversely proportional to the square of...

The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1) = 500. a. [2] Compute T(2,0,0). b. [3] Find the rate of change of T at the point (2,3,3) in the direction of the point (3,1,1). c. [3] What is the maximal rate of change of T at the point (2,3,3)?

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in...

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in July in a town in Colorado. The x distribution has a mean μ of approximately 75°F and standard deviation σ of approximately 8°F. A 20-year study (620 July days) gave the entries in the rightmost column of the following table. I II III IV Region under Normal Curve x°F Expected % from Normal Curve Observed Number of Days in 20 Years μ – 3σ...

a. The probability that the temperature will fall below 32 degrees Fahrenheit on any given day...

a. The probability that the temperature will fall below 32 degrees Fahrenheit on any given day is 20%. If the temperature does fall below 32 degrees, then there is an 80% chance of ice/frost. What is the probability that on any given day, the temperature will fall below 32 degrees and there will be ice/frost? (Input answer as a decimal, rounded to three decimal places if necessary b.In the card game Pokemon, players must construct a 60-card deck to play...

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2...

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e−x2 − 3y2 − 7z2 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, −1, 2) in the direction towards the point (4, −4, 4). answer in °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

The temperature at a point (x, y, z) is given by T(x, y, z) = 300e−x2...

The temperature at a point (x, y, z) is given by T(x, y, z) = 300e−x2 − 3y2 − 9z2 where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, −1, 3) in the direction towards the point (6, −2, 6) (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

1. Temperature in kelvins (K) is related to the temperature in degrees Fahrenheit (°F) by the...

1. Temperature in kelvins (K) is related to the temperature in degrees Fahrenheit (°F) by the equation Design a MATLAB program that will do the following a. Prompt the user to enter an input temperature in °F. b. Read the input temperature. c. Calculate the temperature in kelvins in a separate function d. Write out the results with two digits to the right of the decimal (Use the fprintf function). The results should go to the command window.

Write a program that displays a temperature conversion table for degrees Celsius and degrees Fahrenheit. The...

Write a program that displays a temperature conversion table for degrees Celsius and degrees Fahrenheit. The table should include rows for all temperatures between 0 and 100 degrees Celsius that are multiples of 10 degrees Celsius. Include appropriate headings on your columns. The formula for converting between degrees Celsius and degrees Fahrenheit can be found on the internet. Python 3

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