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:

Madison started hiking at an elevation of 4 meters above sea level. She hiked up at a rate of 3 meters per minute. The graph below represents the relationship between the number of minutes and the elevation. 4 ) What is the slope of the line? slope =

Madison started hiking at an elevation of 4 \mathbf{4} meters above sea level. She hiked up at a rate of 3 \mathbf{3} meters per minute. The graph below represents the relationship between the number of minutes and the elevation. 44 )\newlineWhat is the slope of the line?\newlineslope = =

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Relate position, velocity, speed, and acceleration using derivativesright chevron icon

Full solution

Q. Madison started hiking at an elevation of 4 \mathbf{4} meters above sea level. She hiked up at a rate of 3 \mathbf{3} meters per minute. The graph below represents the relationship between the number of minutes and the elevation. 44 )\newlineWhat is the slope of the line?\newlineslope = =
  1. Identify variables and values: Identify the variables and their values from the problem statement. Madison starts at 44 meters and hikes up at a rate of 33 meters per minute.
  2. Recognize slope calculation: Recognize that the slope of a line in a graph representing a relationship between two variables (time and elevation in this case) is calculated by the change in elevation divided by the change in time, represented as ΔelevationΔtime\frac{\Delta \text{elevation}}{\Delta \text{time}}.
  3. Calculate slope using rate: Calculate the slope using the rate of elevation change per minute. Since she hikes up at 33 meters per minute, the slope is 33 meters per minute.

More problems from Relate position, velocity, speed, and acceleration using derivatives

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t0.7sin⁡(2t+3) v(t)=t^{0.7} \sin (2 t+3) . What is the acceleration of the particle at time t=4 t=4 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t1.1cos⁡(t2−5) v(t)=t^{1.1} \cos \left(t^{2}-5\right) . If the position of the particle is x=−2 x=-2 when t=2.5 t=2.5 , what is the position of the particle when t=1 t=1 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t0.9sin⁡(t−1) v(t)=t^{0.9} \sin (t-1) . If the position of the particle is x=−3 x=-3 when t=3 t=3 , what is the position of the particle when t=5 t=5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t2.1sin⁡(2t) v(t)=t^{2.1} \sin (2 t) . Find all times when the speed of the particle is equal to 22 on the interval 0≤t≤4 0 \leq t \leq 4 . You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer: t= t=
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t2.3+5)sin⁡(2t) v(t)=\left(t^{2.3}+5\right) \sin (2 t) . What is the distance traveled by the particle over the interval 0≤t≤5 0 \leq t \leq 5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t1.9cos⁡(3t−1) v(t)=t^{1.9} \cos (3 t-1) . What is the distance traveled by the particle over the interval 0≤t≤3 0 \leq t \leq 3 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t1.6+3)cos⁡(3t) v(t)=\left(t^{1.6}+3\right) \cos (3 t) . What is the average velocity of the particle on the interval 0≤t≤6 0 \leq t \leq 6 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its acceleration is given by a(t)=(t0.5+3)cos⁡(3t) a(t)=\left(t^{0.5}+3\right) \cos (3 t) . If the velocity of the particle is v=−2 v=-2 when t=1 t=1 , what is the velocity of the particle when t=1 t=1 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t2.1sin⁡(2t+5) v(t)=t^{2.1} \sin (2 t+5) . Find all times when the speed of the particle is equal to 11 on the interval 0≤t≤3 0 \leq t \leq 3 . You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer: t= t=
Get tutor helpright-arrow

Posted 2 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t2.1+5)cos⁡(2t) v(t)=\left(t^{2.1}+5\right) \cos (2 t) . What is the distance traveled by the particle over the interval 0≤t≤5 0 \leq t \leq 5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 2 months ago

View all (149)