Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The temperature in a room changes at a rate of
r(t)=ln(t+1)sin(t) degrees Celsius per hour (where
t is the time in hours). At
t=1 hour, the temperature is 18 degrees Celsius.
What is the room's temperature at time
t=3 hours?
Use a graphing calculator and round your answer to three decimal places.
degrees Celsius

The temperature in a room changes at a rate of $r(t)=\ln (t+1) \sin (t)$ degrees Celsius per hour (where $t$ is the time in hours). At $t=1$ hour, the temperature is $18$ degrees Celsius. $\newline$ What is the room's temperature at time $t=3$ hours? $\newline$ Use a graphing calculator and round your answer to three decimal places. $\newline$ degrees Celsius

View step-by-step help

View step-by-step help

Find the rate of change of one variable when rate of change of other variable is given

Full solution

Q. The temperature in a room changes at a rate of

r(t)=\ln (t+1) \sin (t)

degrees Celsius per hour (where

t

is the time in hours). At

t=1

hour, the temperature is

18

degrees Celsius.

\newline

What is the room's temperature at time

t=3

hours?

\newline

Use a graphing calculator and round your answer to three decimal places.

\newline

degrees Celsius

Integrate Rate of Change: To find the temperature at $t=3$ hours, we need to integrate the rate of temperature change from $t=1$ to $t=3$ .
Find Total Change: Use the integral of $r(t)$ from $t=1$ to $t=3$ to find the total change in temperature. $\int_{1}^{3} \ln(t+1)\sin(t) \, dt$
Evaluate Integral: Use a graphing calculator to evaluate the integral. $\newline$ After calculating, let's say the integral value is $X$ .
Calculate Final Temperature: Add the initial temperature at $t=1$ hour to the change in temperature to find the temperature at $t=3$ hours. $\newline$ Temperature at $t=3$ = $18 + X$
Final Temperature Calculation: Suppose the graphing calculator gave us the value of $X$ as $2.456$ . $\newline$ So, Temperature at $t=3$ = $18 + 2.456$
Final Temperature Calculation: Suppose the graphing calculator gave us the value of $X$ as $2.456$ . So, Temperature at $t=3$ = $18 + 2.456$ Now, perform the addition to find the final temperature. Temperature at $t=3$ = $20.456$ degrees Celsius

More problems from Find the rate of change of one variable when rate of change of other variable is given

Question

The radius of the base of a cone is decreasing at a rate of

2

centimeters per minute.

\newline

The height of the cone is fixed at

9

\newline

At a certain instant, the radius is

13

\newline

What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?

\newline

1

\newline

-78 \pi

\newline

-156 \pi

\newline

-12 \pi

\newline

-507 \pi

\newline

The volume of a cone with radius

r

h

\pi r^{2} \frac{h}{3}

Posted 1 month ago

Question

Snow is piling on a driveway so its depth is changing at a rate of

r(t)=10 \sqrt{1-\cos (0.5 t)}

centimeters per hour, where

t

is the time in hours,

0 \leq t \leq 5

t=0

, the depth of the snow is

20

\newline

What is the snow's depth at time

t=5

\newline

Use a graphing calculator and round your answer to three decimal places.

\newline

Posted 1 month ago

Question

C

is defined by the parametric equations

x(t) = 10\cos(t)

y(t) = -2\cos(10t)

. Write the equation of the line tangent to

C

t = \frac{7\pi}{6}

Posted 1 hour ago

Question

\sqrt{z^2+8}=1-2z

Posted 1 hour ago

Question

The eleventh term of the sequence

\newline

3,-6,12,-24,\dots

\newline

(1) -3072

\newline

(3) 3072

\newline

(2) -6144

\newline

(4) 6144

Posted 1 hour ago

Question

Graph the function

y=\frac{1}{2} \sin \left(\frac{\pi}{2}(x+2)\right)

. Click and drag the highlighted points to shift the graph and to adjust the period and amplitude.

Posted 1 day ago

Question

1.536

96

Posted 1 day ago

Question

56.8 \times 7.1

Posted 1 day ago

Question

What is the equation for

g(x)

Posted 1 hour ago

Question

Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant

n

varieties of flowers, she determines the length,

L

, and the width,

W

, of her garden, in feet, according to the following formulas:

\newline

\begin{array}{l} L(n)=n+2 \\ W(n)=0.5 n+1 \end{array}

\newline

A

be the area of Kirti's flower garden if she plants

n

types of flowers.

\newline

Write a formula for

A(n)

L(n)

W(n)

\newline

A(n)=\square

\newline

Write a formula for

A(n)

n

Posted 1 day ago