Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The function b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t (in minutes). What does int_(0)^(6)b^(')(t)dt=93 mean? Choose 1 answer: (A) At t=6 minutes, the temperature of the brownies is 93 degrees Celsius. (B) The temperature of the brownies increased by 93 degrees Celsius in the first six minutes. (C) During the first six minutes, the temperature of the brownies increases an average of 93 degrees Celsius per minute. (D) At t=6 minutes, the brownies have an instantaneous rate of temperature change of 93 degrees Celsius per minute.

The function b(t) b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t t (in minutes).\newlineWhat does ∫06b′(t)dt=93 \int_{0}^{6} b^{\prime}(t) d t=93 mean?\newlineChoose 11 answer:\newline(A) At t=6 t=6 minutes, the temperature of the brownies is 9393 degrees Celsius.\newline(B) The temperature of the brownies increased by 9393 degrees Celsius in the first six minutes.\newline(C) During the first six minutes, the temperature of the brownies increases an average of 9393 degrees Celsius per minute.\newline(D) At t=6 t=6 minutes, the brownies have an instantaneous rate of temperature change of 9393 degrees Celsius per minute.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Evaluate two-variable equations: word problemsright chevron icon

Full solution

Q. The function b(t) b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t t (in minutes).\newlineWhat does ∫06b′(t)dt=93 \int_{0}^{6} b^{\prime}(t) d t=93 mean?\newlineChoose 11 answer:\newline(A) At t=6 t=6 minutes, the temperature of the brownies is 9393 degrees Celsius.\newline(B) The temperature of the brownies increased by 9393 degrees Celsius in the first six minutes.\newline(C) During the first six minutes, the temperature of the brownies increases an average of 9393 degrees Celsius per minute.\newline(D) At t=6 t=6 minutes, the brownies have an instantaneous rate of temperature change of 9393 degrees Celsius per minute.
  1. Understand Meaning: Understand the meaning of the integral of a derivative function. The integral of a derivative function b′(t)b'(t) over an interval [0,6][0, 6] represents the net change in the function b(t)b(t) over that interval. In this context, b(t)b(t) represents the temperature of the brownies, and b′(t)b'(t) represents the rate of change of the temperature with respect to time. The integral of b′(t)b'(t) from 00 to 66 being equal to 9393 means that the net change in temperature from time t=0t=0 to [0,6][0, 6]00 minutes is 9393 degrees Celsius.
  2. Interpret Choices: Interpret the given answer choices in the context of the integral.\newline(A) This choice suggests that the temperature at a specific time is 9393 degrees Celsius, which is not what the integral of a rate of change represents.\newline(B) This choice suggests that the temperature increased by a total of 9393 degrees Celsius over the first six minutes, which aligns with the meaning of the integral of the rate of change.\newline(C) This choice suggests an average rate of change per minute, which is not directly related to the integral of the rate of change over a time period.\newline(D) This choice suggests an instantaneous rate of change at a specific time, which is not what the integral represents; it represents the total change over an interval.
  3. Choose Correct Answer: Choose the correct answer based on the interpretation of the integral. The correct interpretation of the integral from 00 to 66 of b′(t)extdtb'(t) ext{ dt} equal to 9393 is that the temperature of the brownies increased by a total of 9393 degrees Celsius over the first six minutes. Therefore, the correct answer is (B)(B).

More problems from Evaluate two-variable equations: word problems

Question
This equation shows how the distance traveled by a car is related to the time spent driving. d=50t+10 d = 50t + 10 . The variable t t represents the time in hours, and the variable d d represents the distance in miles. How far does the car travel in 2 2 hours?
Get tutor helpright-arrow

Posted 9 months ago

Question
The equation shows how the cost of buying pencils is related to the number of pencils purchased. \newline c=0.5p+2 c= 0.5p+2 \newlineThe variable p p represents the number of pencils, and the variable c c represents the total cost. How much does it cost to buy 10 10 pencils?
Get tutor helpright-arrow

Posted 9 months ago

Question
This equation shows how the total score in a game is related to the number of points scored per level. s=100l+250 s = 100l + 250 . The variable l l represents the levels completed, and the variable s s represents the total score. What is the total score after completing 3 3 levels?
Get tutor helpright-arrow

Posted 7 months ago

Question
The equation shows how the amount of paint needed is related to the area to be painted. p=2a+5 p = 2a + 5 . The variable a a represents the area in square meters, and the variable p p represents the amount of paint in liters. How much paint is needed for an area of 8 8 square meters?
Get tutor helpright-arrow

Posted 7 months ago

Question
This equation shows how the total bill for a meal is related to the number of people sharing the meal. \newline b=15n+35 b = 15n + 35 \newlineThe variable n n represents the number of people, and the variable b b represents the total bill. What is the total bill for a meal shared by 4 4 people?
Get tutor helpright-arrow

Posted 9 months ago

Question
Poppy the dog weighs p p pounds, and Yumi the cat weighs y y pounds. If Poppy weighs 3636 more pounds than Yumi does, which of the following equations correctly describes the relationship between their weights?\newlineChoose 11 answer:\newline(A) p+y=36 p+y=36 \newline(B) p+36=y p+36=y \newline(C) p−y=36 p-y=36 \newline(D) y−p=36 y-p=36
Get tutor helpright-arrow

Posted 7 months ago

Question
Calvin and Melvin are two of Santa's elves. The number of toys they build is given by 11c+8m 11 c+8 m , where c c is the number of candy canes Calvin eats for breakfast and m m is the number of candy canes Melvin eats for breakfast. How many toys do they build when Calvin eats 55 candy canes and Melvin eats 33 candy canes for breakfast?
Get tutor helpright-arrow

Posted 7 months ago

Question
2w+4 2 w+4 \newlineCarly is cutting a piece of paper stock based on the width of a photo. The expression above describes the length of the paper stock, in inches, for a photo that is w w inches wide. If the photo is 88.55 inches wide, what is the length of the paper stock in inches?
Get tutor helpright-arrow

Posted 7 months ago

Question
Calvin and Melvin are two of Santa's elves. The number of toys they build is given by 11c+8m 11 c+8 m where c c is the number of candy canes Calvin eats for breakfast and m m is the number of candy canes Melvin eats for breakfast.\newlineHow many toys do they build when Calvin eats 55 candy canes and Melvin eats 33 candy canes for breakfast?\newlinetoys
Get tutor helpright-arrow

Posted 8 months ago

Question
The approval rating of a certain politician is changing at a rate of r(t) r(t) percent of the population per month (where t t is the time in months).\newlineWhat does ∫03r(t)dt \int_{0}^{3} r(t) d t represent?\newlineChoose 11 answer:\newline(A) The rate of change of the approval rating of the politician when t=3 t=3 months\newline(B) The average rate of change of the approval rating during the first three months\newline(C) The change in the percent of the population who approves of the politician during the first three months\newline(D) The percent of the population who approves of the politician when t=3 t=3 months
Get tutor helpright-arrow

Posted 7 months ago

View all (180)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant