HW17-relatedratescircuitKEY

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Roosevelt High School, Roosevelt**We aren't endorsed by this school

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MATH CALCULUS

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Physics

Date

Dec 19, 2024

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Uploaded by ChancellorAlligator4719

Circuit Training - Related Rates Name \’(\E \'{ Directions: Beginning in cell #1, read the problem, identify the key information, and sketch a helpful picture. Decide what formula relates all of your information, and differentiate it with respect to t. Finally, answer the question and search for it to advance in the circuit. Mark that cell #2 and continue in this manner until you complete the circuit. Note: Technology should be used in the final stages of solving. Round all answers to three decimal places, but hold intermediate values to at least five decimal places. Answer: 1.185 #__1__ Arectangle’s base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the area changing, in cm?/min, when the heightis 1.5 cm? G‘i\/e.‘“\" b__ = o N A — b\’\_ " c:U-\ d n d =195 C—"fi/fi‘\\ ™\ ot \{\,:\‘50“"\ AA SL\ S) i O c:.,“l"\ =N Answer; 1.035 7 Co A spherical balloon is losing air at a rate of 2500 cm3/sec. What is the radius, in cm, when it is \_...--"' changing at a ratfie of 25 cm/sec? E oA O 40O N G wen N ...___._,_,4 o dY _ _ozooem/e V= Sfir\l.. &t d\( r?'- S A - 2B cm = =4 rt dt L = okt r2S at < T 2BDD “ = Siad ¥ BPT = = T \= 9’(‘2‘\“‘“ | T Answer: (.750 H el A rectangle’s base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the perimeter changing, in cm/min, when the height is 1.5 cm? Given. bzBaom P=2Zn+2b Zo =05 e/ d . '2_—-"-'&-&9—- A dx ’ e e a—— ] _.c}..?_t'bficm YO T /A e e © Virge Cornelius 2015

Answer: 4.909 5 l Two snails start moving away from each other from the same point in a garden. One travels north at a rate of 10 cm/hour and the other travels east at a rate of 3 cm/hour. After two hours, how fast is the distance between the snails changinE, in cm/hour? Given Fiacd d‘?t‘ L ' P - A A% _ o™ Eauveation i X T =z N. 3~ ™n Tdx nyd8 Rz 3T ) 9 X = E \%%QEJF A9t OLZ:E | = nr G (>)+ 2@(10>1J436 E"Et__ - _ Z, X ‘5_25 Jfi%fi:%b?’;lo.%o%) (35 T > Ja->e Answer: 3.000 # 27 A right triangle has legs x and y and hypotenuse z. At what rate is leg x changing, in cm/min, wheny =4 cm, dy/dt=1.2 cm/min,z =5 cm, and dz/dt = 3.4 cm/min? Given.y=4 Eowatbion -5 N | d - - ".1"---_1' Y __.Z*:\.Rt.m X = T~ 4 | K /me\ du? Ld*" -:::\S( 3-3: TTX=D %%-"-'54 ey vAxq002) =504 Ao e A —110 - 9D Fiodr 3¢ C%x:q_gm cm—‘:fi -JL% = 4,067 Answer: 10.440 # 10O The volume of a cube is 125 ¢m3 and is changing at a rate of 8 cm3/sec. How fast is the surface area changing, in cm?2/sec, at that moment in time? : ) , Given Eopation St [ oe T V=S c;f‘“:" SA= 6% (;(,: x| A ox %:%omaeu dfﬂ:lz%ég "5‘.;(:'30( 3t li X = D \5 c‘gt dt o 5(‘?-5)% e 92 LB. - ) Ao _ % oo 42 c.\sc}d: 3;& >(®%5 ¥ 715 dt T E T o™ Lo © Virge Cornelius 2015

Answer: 4.067 8 < A 13-foot ladder slides down an exterior wall at a rate of 1 ft/sec. How fast is the distance between the base of the ladder and the base of the wall changing, in ft/sec, when the base of the ladder is 5 ft from the base of the wall? Equm-%-\om Given: n * ‘3 V24 9 R /A X+5 N - Z -\ \BY xfifi [ xX=5 5&9&. _ \Q_'—‘cg L AX :lfié'- d.;c Cj:bfx,_ \(:— "ad\ -‘;--\'/JB- at Answer: 2.821 g Charlie Brown flies a kite at a constant height of 100 feet while the wind carries the kite away from him horizontally at rate of 2 ft/sec. How fast must he release the string from the spool, in ft/sec, when the kite is 300 feet away from him (i.e. when he has let out 300 feet of string)? 1(‘2&)9 ?) 300&% ‘\ d;: "422‘:-“’ \\ B B0 'g""/u;z._ Answer: 2.400 i3 >, A circle is expanding at a rate of 32.5 cm2/min. How fast is the radius changing, in cm/min, when the circumference is 10w cm? . E_ b‘t_&-\-{ O N Given: &A . x9S A - o A =T At T A cL C=ziom= &8 S = 2T &_tcL - 5 5o €= D S oD FI}p y Q° B 2 A e VS AALODD e " = ‘Et ™YY ™ d ~'C © Virge Cornelius 2015

Answer: 6.400 # \ \ A conical paper drinking cup has a height of 6 inches and a radius of 2 inches (at the top). How fast is the water level in the cup rising if water is poured in at a rate of 1 in3/sec and the water is 2 inches deep? iwvent \ = -1:5 TT ("m\'k o\ = — U b—-—-:‘- :E n el V=TE ()" = 2H n-—d\;\_ ah ‘== () g=x — Jt A an 5 N AT \n_/ e 4w\ = Answer: 0.716 H | "2 Profit is Revenue - Cost. A manufacturing plant calculates its Cost function, C(x), to be C(x) =x3 - 4x%2 + 50/x and its Revenue function, R(x), to be R(x) = 50x. Construct the profit function, P(x), and determine the x-value when dP/dt is 4.544 and dx/dt = 0.05. ‘ P(D= 500 - (x-a0l + 32 = 50m~ ¥4~ 200 I _ 2ot 0% L 559X 4 5O dox d‘&i‘ = 30Tk T X W I 5 Ok 30 (\05) _,3;-)(%(‘{:)5)-#-%()( (*DS>+ _521 ) + . QoL -—72—5'_ 4 =447 50(-*(35) 4.549 = 2.5 = 15% rx:h\%‘?: Answer: 1.886 # CE Salt for winter road maintenance is poured so that it forms a conical pile such that the radius is twice the height. Find the rate at which the pile is growing, in ft3/hour, when the radius is changing at a rate of 0.5 ft/hour and measures 2 | o - ' ifﬂfit‘\[ d\}r H-C(' - \ Griven "h-: -—i 'Ft ~ LY -(;E‘-E: —";:-LQ\E)) (‘5/ ¢ = 2Ny dt — S de s 8 Egquatioo; AV 4 qoq<t gt Vs v 5Tl . — = 2.5 V=% (7 - ¢ = . \[ Co lép w T at P.S. Of course | know how unlikely these crazy questions are! You have to practice them anyway! © Virge Cornelius 2015