X 78dodo..: "Out of a violet mou X + Abc ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied1 0 H Men Custom Suits... OBCHASEME.. O SRRHHRS 20... b Big Dude USA - Bi... 20 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Math Editor Saved! Erase Edit Qia 3 10 Applied related rates Exercise. Reveal Hint A 12 foot ladder is leaning against a wall. At the instant that the foot of the ladder is 3 feet away from the wall, the foot of the ladder is moving away from the wall at a rate of 5 . At what rate is the top of the ladder falling down the wall at this time? The top of the ladder is falling at a rate of ? feet per second. Previous Next -> Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera teamX 3ce348..: "Past the heavy cub x + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied1a H Men Custom Suits... O BASEXX... 0 9:28x($ 20... Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia Exercise. It is afternoon. How fast is the length of the shadow of a 72 ft tall tree changing when 0, the angle of elevation of the sun, is -? Assume Reveal Hint that the rate at which the angle of elevation is decreasing is 0.25 rad/hr. STEP 1 Introduce a variable x that denotes the length of the shadow of the tree. Then sketch and label the figure. STEP 2 Complete the following statements. The known rate is rad/hr The rate to be determined is when 0 =- STEP 3 Write an equation that relates all relevant variables. tan(0) = STEP 4 Differentiate both sides of the equation above with respect to t (differentiate the left side first). d ? ? d atX 3ce348..: "Past the heavy cub X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied1a H Men Custom Suits... O BASEXX... O SHERHAS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia Write an equation that relates all relevant variables. tan(0) = STEP 4 Differentiate both sides of the equation above with respect to t (differentiate the left side first). ? d ? d It STEP 5 Evaluate. Now, in order to evaluate the equation at the instant when 0 = -, we have to find the value of x at that instant! tan () - tan ? STEP 6 Solve for a x -" ? ft/ hr .X 895da0..: "Between the dark t x + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied2 H Men Custom Suits... O BASEME.. O BERHERS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA @ in 6 hours Get Help Save Erase Edit Qia 10 w Applied related rates Exercise. Reveal Hint A colony of bacteria are growing in a petri dish. They form a circular disk, which appears to be growing at a rate of 4 square millimeters per hour. When the radius of the disk is 3 millimeters, at what rate is the radius growing? At this instant, the radius of this disk is growing at a rate of ? millimeters per hour. - Previous Next -> Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera teamX 979b85..: "Alongside the free x + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied6 H Men Custom Suits... O BABEME.. O SRRHHRS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA @ in 6 hours Get Help Math Editor Saved! Erase Edit Qia 4 10 Applied related rates Exercise. A light on the ground is 30 feet away from a building. A 5 foot tall man is walking from the light to the building at a rate of 3 feet per second. He is casting a shadow on the side of the building. At what rate is his shadow shrinking when he is 10 feet from the building? His shadow is shrinking at a rate of ? feet each second. Previous Next > Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera teamX 9b5a03..: "Pursuant to a bitter X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied77 H Men Custom Suits... O BASEXX... @ SHEERS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Save Erase Edit Qia Exercise. Reveal Hint A bug is moving along the curve y = va and its altitude is increasing at the rate of 4ft/s. Here, x and y are both measured in feet. How fast is the distance of the bug from the origin changing at the moment when the bug is v12 ft from the origin. STEP 1 Introduce a variable D denoting the distance of the bug from the origin. Sketch and label a figure. STEP 2 Complete the following statements. The given rate is = 4ft/s The rate to be determined is , when D = V12 ft Write an equation relating variables x, y, and D. D2 = STEP 3 Differentiate. 2D . - d d + 2X 9b5a03..: "Pursuant to a bitter X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied77 H Men Custom Suits... . BASEXX... 0 9RRHHRS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia STEP 3 Differentiate. 2D d d . X + 2 . Simplify. D . d = x d + STEP 4 Evaluate. In order to evaluate d D] JD=V12' We have to evaluate [x ] D=V12 = [y]D=V12 = ? ft (1) d = 29 . at ] D=12 (2 ) ? ft / s (3) Therefore,X 9b5a03..: "Pursuant to a bitter X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/relatedRatesApplied77 H Men Custom Suits... O SHARE.. 0 9:3HR($ 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia D . d d d dt = x . at + dt STEP 4 Evaluate. In order to evaluate d D _ we have to evaluate [ x] D=V12= [ylD=V12 = ? f (1) = |24 . at ] D= V12 (2) = ? (3) Therefore, J D=VIZ = 3 . 8V/3 + V3 and ft / sX c3baec..: "Below the comforta X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/singVarCalcRelatedRates1 H Men Custom Suits... O BRASEX.. O SRRHEXIS 20... b Big Dude USA - Bi... 20 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Save Erase Edit Qia 3 10 Applied related rates Exercise. A cylindrical tank standing upright (with one circular base on the ground) has radius 20 cm. How fast does the water level in the tank drop when the water is being drained at 25 cm3/sec? cm/s Previous Next > Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera team 100 Math Tower, 231 West 18th Avenue, Columbus OH, 43210-1174X 87254b..: "As the quiet approx X + - C ximera.osu.edu/mooculus/appliedRelatedRates/exercises/exerciseList/appliedRelatedRates/exercises/singVarCalcRelatedRates9 H Men Custom Suits... OSHASENSE.. O BREEHAS 20... b Big Dude USA - Bi... 70 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Math Editor Saved! Erase Edit Qia 3 10 Applied related rates Exercise. A balloon is at a height of 50 meters, and is rising at the constant rate of 5 m/sec. A bicyclist passes beneath it, traveling in a straight line at the constant speed of 10 m/sec. How fast is the distance between the bicyclist and the balloon increasing 2 seconds later? ? m/s Previous Next > Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera team 100 Math Tower, 231 West 18th Avenue, Columbus OH, 43210-1174X 87254b..: "As the quiet approx x X 735125..: "Because of the brig X + - C ximera.osu.edu/mooculus/moreThanOneRate/exercises/exerciseList/moreThanOneRate/exercises/relatedRatesSimple3 0 ... H Men Custom Suits... O BASE... O SHERHERS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Save Erase Edit Qia Exercise. A circle is expanding. At time to, its radius is 2m, and is growing at a rate of 4-9. At what rate is its area growing at the time to? SOLUTION: Let A be the area, and r be the radius of the circle. The given rate is dr V = 4 dt S The rate to be determined is d A dt It=to The equation relating A and r is A =TM^2 Differentiating with respect to time, we have dA = TT dt d.tX 87254b..: "As the quiet approx x X 591dfe..: "Pursuant to the clev X + - C ximera.osu.edu/mooculus/moreThanOneRate/exercises/exerciseList/moreThanOneRate/exercises/relatedRatesSimple4 0 H Men Custom Suits... OSHASEX... 0 9:28x($ 20... b Big Dude USA - Bi... 20 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia Exercise. Reveal Hint An isosceles triangle has side lengths r, r and 2. The angle between the sides of length r is 0. If r is increasing at a rate of 3 units when r = 2, then at what rate is the angle changing at that time? SOLUTION: The given rate is dr V =3 units dt S The rate to be determined is Draw a picture. It should be clear from your picture that r and 0 satisfy the relation sin(? = Differentiating implicitly with respect to time, d 2 cos -1 ? at Note that at the time when r = 2,X 87254b..: "As the quiet approx x X 591dfe..: "Pursuant to the clev x + - C ximera.osu.edu/mooculus/moreThanOneRate/exercises/exerciseList/moreThanOneRate/exercises/relatedRatesSimple4 H Men Custom Suits... O BASEXX.. O RRHAS 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight... a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XIMERA in 6 hours Get Help Save Erase Edit Qia sin (2 = ? Differentiating implicitly with respect to time, d d. ? cos( ? - 1 dt at Note that at the time when r = 2, [0]r=2 = , SO 1 do -1 COS 3) dt r=2 ? Solving for at we have = rad dt r=2 S - Previous Next >X 87254b...: "As the quiet approx x X fee52b..: "Due to a powerful s( X + - C ximera.osu.edu/mooculus/moreThanOneRate/exercises/exerciseList/moreThanOneRate/exercises/relatedRatesSimple6 H Men Custom Suits... OBAMASEX.. O BRAH 20... b Big Dude USA - Bi... 50 DOKV a Amazon.com: OA... a DXL Twenty-Eight. a Amazon.com: DXL a Amazon.com: ZHILI a Amazon.com: Car... XINERA in 6 hours Get Help Save Erase Edit Qia More than one rate Exercise. Reveal Hint A rectangular prism with a square base is deforming in such a way that it maintains a constant volume. At the instant that its height is 4, the length of its base is 5, and its length is shrinking at a rate of 3 's, what is the rate of change in the height of the box? ? units S - Previous Next > Courses About Social Built at The Ohio State University Calculus One FAQ Facebook f with support from NSF Grant DUE- Calculus Two Development Team Twitter y 1245433, the Shuttleworth Calculus Three Workshop Google Plus G+ Foundation, the Department of Contact Us GitHub @ Mathematics, and the Affordable Learning Exchange. THE OHIO STATE UNIVERSITY 2013-2023, The Ohio State University - Ximera team