/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 51 A patient's temperature was \(97... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 51

A patient's temperature was \(97.0^{\circ} \mathrm{F}\) at 8: 05 A.M. and \(101.0^{\circ} \mathrm{F}\) at 12: 05 P.M. If the temperature change with respect to elapsed time was linear throughout the day, what would the patient's temperature be at 3: 35 P.M.?

Short Answer

Expert verified
Answer: The patient's temperature would be approximately 103.8掳F at 3:35 P.M.

Step by step solution

01

Convert given times to a common format

First, convert the given times to minutes elapsed since midnight to make calculations easier. 8:05 A.M. is 485 minutes since midnight, and 12:05 P.M. is 725 minutes since midnight.
02

Calculate the slope of the temperature change

Using the given temperatures, calculate the slope (rate of change) by subtracting the two temperature values and dividing by the time difference. Let \(x\) represent the time in minutes since midnight and \(y\) represent the temperature in Fahrenheit. Slope, denoted by \(m\): \[m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{101 - 97}{725 - 485} = \frac{4}{240}\]
03

Calculate the temperature at 3:35 P.M.

To find the patient's temperature at 3:35 P.M., first convert the time to minutes past midnight. 3:35 P.M. is 895 minutes since midnight. Now we will use the slope-point equation of the line: \[y - y_1 = m(x - x_1)\] Using the coordinates (485, 97) and the slope, 1/60, we have: \[y - 97 = \frac{1}{60}(x - 485)\] Plug in 895 for x to find the patient's temperature at 3:35 P.M.: \[y - 97 = \frac{1}{60}(895 - 485)\] \[y - 97 = \frac{1}{60}(410)\] \[y - 97 = 6.83\] \[y = 103.83\] So the patient's temperature would be approximately \(103.8^{\circ} \mathrm{F}\) at 3:35 P.M.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The average speed of a nitrogen molecule in air is proportional to the square root of the temperature in kelvins \((\mathrm{K}) .\) If the average speed is \(475 \mathrm{m} / \mathrm{s}\) on a warm summer day (temperature $=300.0 \mathrm{K}\( ), what is the average speed on a cold winter day \)(250.0 \mathrm{K}) ?$
An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by \(50 \%,\) and increase the height by \(20 \% .\) By what factor has the volume of the room increased?
A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 2.0 during this procedure, by what factor does the radius of the balloon change? (tutorial: car on curve)
In a laboratory you measure the decay rate of a sample of radioactive carbon. You write down the following measurements: $$\begin{array}{lrrrrrrr} \hline \text { Time (min) } & 0 & 15 & 30 & 45 & 60 & 75 & 90 \\\ \text { Decays/s } & 405 & 237 & 140 & 90 & 55 & 32 & 19 \\\ \hline \end{array}$$ (a) Plot the decays per second versus time. (b) Plot the natural logarithm of the decays per second versus the time. Why might the presentation of the data in this form be useful?

Some thieves, escaping after a bank robbery, drop a sack of money on the sidewalk. (a) Estimate the mass of the sack if it contains \(\$ 5000\) in half- dollar coins. (b) Estimate the mass if the sack contains \(\$ 1000000\) in \(\$ 20\) bills.
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Magnetism

Read Explanation

Kinematics Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.