5

QUESTION 7AArea of circle radius Of circle Tr2If the area of a circle Is Increasing at the rate ofcm? 10 secfind the rate (cm/sec) at which the radlus of that circl...

Question

QUESTION 7AArea of circle radius Of circle Tr2If the area of a circle Is Increasing at the rate ofcm? 10 secfind the rate (cm/sec) at which the radlus of that circle Is Increasing when the radlus Is 3 crL:Just put the number part ol your answcr, accurate t0 at leust decImal places; In the onswer box So; If your answer is 1.123 cm/sec, put ; 123 In the Onswer bwox

QUESTION 7 A Area of circle radius Of circle Tr2 If the area of a circle Is Increasing at the rate of cm? 10 sec find the rate (cm/sec) at which the radlus of that circle Is Increasing when the radlus Is 3 crL: Just put the number part ol your answcr, accurate t0 at leust decImal places; In the onswer box So; If your answer is 1.123 cm/sec, put ; 123 In the Onswer bwox



Answers

Area The radius $r$ of a circle is increasing at a rate of 3 inches per minute. Find the rates of change of the area when (a) $r=6$ inches and (b) $r=24$ inches.

In the question we have to find the rate of change of area of a circle with respect to each radius R. When for the party are is three cm and in part we are is 4cm. Now moving towards this solution. Now consider X denote the area of the circle with the radius R. So the area of the circle will be called to buy our square. Now the rate of change of area that is X. With respect to R. S. Dx by D. R. That is pie into to our which is two pi R. Now moving further for the party where are well with three centimeter. Your D X by D R will be equal to to buy into three which is 65 square centimetres. Now in part B where our value is four cm or DX by D. R. will be equal to eight pi centimeter square. Thank you.

In the question it has given the radius of our circulars increasing uniformly at the rate of 3cm but seconds And the rate at which the area of the circle is increasing when the radius is 10 cm, we have to find this. Now moving towards the solution, consider x centimeter with the radius of the circle at time. Take So the rate of increase of radius of the circle is three cm/s. This is given to us so D. X by DT is positive. Is positive and equal to three cm. Work second. Now moving further. Consider why as the area of the circle survive will be equal to buy yards square. And rate of change of area of a circle will be given by D by by DT which is by D by D. T. Of X square. So buy into two weeks. Dx by data will be equal to five X. Into three. With that is 65 X. Now moving further. Now put X equals to 10 centimeter has given in the question. So divide by detail will be equal to six by into 10, Which is 65 cm sq/s. Now, as divide by DT is positive. Therefore, surface area is increasing at the rate of 65 cm sq/s. Thank you.

I love related rates problems. This is another one. They're not a big deal on this problem. They tell me that I have a circle with area A. And radius R. And the radius is changing. The radius is increasing so the area is too. So part A says draw a picture of a circle with area and radius R. Part B is write an equation describing the relationship between A and R. We learned in earlier school A equals pi R square. See says, take the derivative of the equation and be with respect to T. I get D A. D. T. The derivative of aid to the first is A. To the zero times the derivative what's inside D. A. D. T. The derivative of the right sound is pie the derivative of two R squared with respect to T. Is to our D. R. D. T. I'm not taking the derivative with respect to our but with respect to T. It's usually written D A D. T. Is equal to pi R D. R. DT. This is the circumference times a teeny tiny change in our, so the area is changing. You can kind of think about this as a really small rectangle that's stretched out and being added to the outside. It's the circumference times a teeny thickness D. R. D. T. See circumference times drd t. Okay so I start with a picture. I read an equation relating the variables they tell me I differentiated implicit implicitly with respect to R. And then I plug in values For part d. They said at the point in time when our is 5cm D. R. DT Is two cm per second meaning the radius is changing at that rate. They want me to find D. A. D. T. At this point I'm just plugging in numbers two times pi times five times two. If I look at the units multiplied centimeters times centimeters per second. So I get centimeters squared per second which is a change in area with time. So I end up with five times two times 2 20 pie centimetres squared per second. They may use a calculator to get a Number value for that. It will be 62.8 and change Because two pi is two times 3.14 mm 4159. That would be 318 maybe. I don't know how many Places after the decimal. They want to carry that one. In calculus we carry three or more places. So that's 20 times pi. I'm checking with my calculator 62.83185. So that could round anywhere you wanted it. Hope that helps. Have a nice day.

Part A wants us toe label the radius an area of the circle. And, um, Harby wants us to relate the equation, tying together these two variables. So the area in this case is equal to I times the radius squared part c asks us to relate the a d t a d r d t So basically taking the derivative of the equation from part B that's going to get us one de a d t. And then using the power war, the two will come in front. And so this will be to i r and then br DT and then lastly, uh, parte de at the instant when the radius is five and the, uh, radius is increasing at a rate of two centimeters her second. We want to know how fast is the area increasing? And so we could substitute these values for the R. D. T two and the radios five and then multiplying all or these values Together we'll get four times 5 20 pie and so part D. Given this information, the radius will increase at 20 Pie centimeters square her second, and that's it


Similar Solved Questions

5 answers
Iwant to makc 1.0 litcr of a buffer that will kccp the pH of a solution at 7.40. If I start by dissolving 30 g of sodium dihydrogen phosphate in watcr; how many milliliters of cither 0.50 M HCL, or 0.SOM NaOH will have to add to this solution to makc my buffer? (6 pts) For phosphoric acid: Kap 7.11 *10" Kaz - 6.32 * 10 ; Kaz - 4.5 * 10-13
Iwant to makc 1.0 litcr of a buffer that will kccp the pH of a solution at 7.40. If I start by dissolving 30 g of sodium dihydrogen phosphate in watcr; how many milliliters of cither 0.50 M HCL, or 0.SOM NaOH will have to add to this solution to makc my buffer? (6 pts) For phosphoric acid: Kap 7.11 ...
5 answers
El Find the inverse of a - 1 in Q(a) where a is a root of f (2) = 24 + 2 + 2.
El Find the inverse of a - 1 in Q(a) where a is a root of f (2) = 24 + 2 + 2....
5 answers
The sessments Select 8 8 } 3 31 parabolic Iniormation ~ 4 4 ~c signal =1. 21: 21 : ;t< t= 3 ceoztia time domain ssessmem can ; represented AtdetanaPayment Contin _
The sessments Select 8 8 } 3 31 parabolic Iniormation ~ 4 4 ~c signal =1. 21: 21 : ;t< t= 3 ceoztia time domain ssessmem can ; represented Atdetana Payment Contin _...
5 answers
Asoluticn ofhydochlonic acidM BCL What 1s the bydrontum-Icn conccntration 25PC7 Wi the hydroridc-ion conccntration z 25'C?[B,0*/ -[OH
Asoluticn ofhydochlonic acid M BCL What 1s the bydrontum-Icn conccntration 25PC7 Wi the hydroridc-ion conccntration z 25'C? [B,0*/ - [OH...
5 answers
Whhat ar 1 What V punt of the tbe FORMULA 1 carbon llowing reaction 1 Reky Entira Group reagent for the H 10.6 grams Fcmaln dloxide 1 otegoup HL complete carbon () [cact With : 1 grams of carbon 1 L
Whhat ar 1 What V punt of the tbe FORMULA 1 carbon llowing reaction 1 Reky Entira Group reagent for the H 10.6 grams Fcmaln dloxide 1 otegoup HL complete carbon () [cact With : 1 grams of carbon 1 L...
5 answers
Express the given equations in logarithmic form.$$2^{-6}= rac{1}{64}$$
Express the given equations in logarithmic form. $$2^{-6}=\frac{1}{64}$$...
5 answers
Consider the DE PG-)y' ` Ay 0, where Use P(x) and 9(x) are both noeborrobeksan o Ghotn Gontinuo continuous cannot % Ihe interval [-2, 6}: chorcosbotpbe soxutions to thas DE on ad Ya I-x ol p(x) and q(x) (hls Interval, regardless of the
Consider the DE PG-)y' ` Ay 0, where Use P(x) and 9(x) are both noeborrobeksan o Ghotn Gontinuo continuous cannot % Ihe interval [-2, 6}: chorcosbotpbe soxutions to thas DE on ad Ya I-x ol p(x) and q(x) (hls Interval, regardless of the...
5 answers
Determine whether O not the vector field F (€,y,2) = In y; E + Inz. % is conservative. If it is conservative; find a function f such that F = Vf.
Determine whether O not the vector field F (€,y,2) = In y; E + Inz. % is conservative. If it is conservative; find a function f such that F = Vf....
5 answers
DETAILSThe volume of the surface generated by rotating the function f(r) 7 (21) aroulid the I-ak 5{GultA4t
DETAILS The volume of the surface generated by rotating the function f(r) 7 (21) aroulid the I-ak 5 { GultA4t...
5 answers
Find the volume of the parallelepiped determined by thevectors a, b,and c.a = ‹5, 3, -3›, b = ‹0, 2, 2›, c = ‹4, -1, 6›
Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ‹5, 3, -3›, b = ‹0, 2, 2›, c = ‹4, -1, 6›...
5 answers
3Etails Hot Llera suttac0 4io2 lnerconanaht cliculr cant ' Qerieratod (uyolyIn? Uc ngion bourdco4radbouZol (ncing GiaunntnrallowcdIntegrationond inqiudingintogralldgHjotk Fux Incluaa Kcpe nccosm0ny
3Etails Hot Llera suttac0 4io2 lnercona naht cliculr cant ' Qerieratod (uyolyIn? Uc ngion bourdco 4ra dbou Zol (ncing Giaunntnr allowcd Integration ond inqiuding intogralldg Hjotk Fux Incluaa Kcpe nccosm0ny...
5 answers
VI IFI 8ji LI'Lji I :1 1 1| 1 3 1 L V 1 8 j + Wt € 8 { 6 1 1 1 WW Ii 3 1 f IL 1 ! ! 1 2 1 8 { i 3 3 2 [ i 1 V W Ff L Eee EEi @E L 1 NL I 1 3 1 2 4 1 1 9 0 1 2 0 + 8 ! 3
VI IFI 8 ji LI'L ji I : 1 1 1| 1 3 1 L V 1 8 j + Wt € 8 { 6 1 1 1 WW Ii 3 1 f IL 1 ! ! 1 2 1 8 { i 3 3 2 [ i 1 V W Ff L Eee EEi @E L 1 NL I 1 3 1 2 4 1 1 9 0 1 2 0 + 8 ! 3...
5 answers
Damage to the sinoatrial node in humans would Select one: block conductance between the bundle branches and the Purkinje fibers b; have negative effect on peripheral resistance disrupt the rate and timing of cardiac muscle contractions have direct effect on blood pressure monitors in the aorta
Damage to the sinoatrial node in humans would Select one: block conductance between the bundle branches and the Purkinje fibers b; have negative effect on peripheral resistance disrupt the rate and timing of cardiac muscle contractions have direct effect on blood pressure monitors in the aorta...
5 answers
Prove that the set {1, cos X, cos 2x, '} is orthogonal on the interval [~n,n].Express the polynomial z2 + x _ 1 in terms of the base {1, €, (3x2 _ 1)}
Prove that the set {1, cos X, cos 2x, '} is orthogonal on the interval [~n,n]. Express the polynomial z2 + x _ 1 in terms of the base {1, €, (3x2 _ 1)}...
5 answers
B.Hair hasapH of 5.0 so the pH of pH balanced shampoo ranges from 5 to 7.At PHz, Is the acid and is the conjugate base: There would be acid than conjugate base_ Check three boxes,cysteine with charge (blank 1)cysteine with charge (blank 1)cysteine with charge (blankcysteine with charge (blank 1)cysteine with +1 chargc (blank 2)cysteine with charge (blank 2)cysteine with charge (blank 2)cystelne with *2 charge (blank 2)More (blank 3)Same (blank 3)Lcss (plank 3)
b.Hair hasapH of 5.0 so the pH of pH balanced shampoo ranges from 5 to 7.At PHz, Is the acid and is the conjugate base: There would be acid than conjugate base_ Check three boxes, cysteine with charge (blank 1) cysteine with charge (blank 1) cysteine with charge (blank cysteine with charge (blank 1)...

-- 0.022871--