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Struggling with solving RELATED RATES word problems? Struggle no more! Math with Professor V
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Solving four related rates problems from Calculus 1.
1. Water is falling on a surface, wetting a circular area that is expanding at a rate of 7 mm^2/s. How fast is the radius of the wetted area expanding when the radius is 152 mm?
2. A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same time, and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point is changing at 5 m^2/s, then how fast are the people moving when they are 4 m from the right angle?
3. The volume of a sphere is increasing at rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4pi/3 cm^3.
4. The volume of a rectangular box with a square base remains constant at 500 cm^3 as the area of the base increases at a rate of 6 cm^2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long.
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1. Water is falling on a surface, wetting a circular area that is expanding at a rate of 7 mm^2/s. How fast is the radius of the wetted area expanding when the radius is 152 mm?
2. A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same time, and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point is changing at 5 m^2/s, then how fast are the people moving when they are 4 m from the right angle?
3. The volume of a sphere is increasing at rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4pi/3 cm^3.
4. The volume of a rectangular box with a square base remains constant at 500 cm^3 as the area of the base increases at a rate of 6 cm^2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 15 cm long.
Don't forget to LIKE, Comment, & Subscribe!
xoxo,
Professor V
Calculus 2 Lecture Videos on Integration:
Trig Review:
Calculus 3 Video Lectures:
#mathwithprofessorv #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos #integrationbyparts #integralcalculus
Join this channel to get access to perks:
Socials:
IG: @mathwithprofessorv
TikTok: @mathwithprofessorv
I'm also an Amazon influencer, so feel free to support and shop:
EXCITING NEWS: You can now sign up for my Patreon at the link below!
My Patreon is a place for students to have access to exclusive ad-free content not available on my YouTube channel! Access to the library of additional videos, worksheets, and more is available with the "Star Pupil Package" tier for just $9.99/month (USD).
*This video is copy protected and cannot be downloaded or used in any capacity without my permission.*
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