VA HW#15 Ch3.6 Implicit differential x Mathway | Algebra Problem Solv( X + X C a webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762586_0 I K 1. [-/22 Points] DETAILS BERRAPCALCBR7 3.6.027.MI.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise For the equation, find -evaluated at the given values. x2 + y2 = xy + 63 at x = 9, y= 3 Step 1 dx We want to find -by implicit differentiation and evaluate at the given point. To do so, we take the derivative of both sides of the equation, staring with the left hand side. View y as a function of x and take the derivative with respect to x. Recall that every time you take the derivative of y to multiply by -, using the Generalized Power Rule. d [ x 2 + y 2] = dx Submit Skip (you cannot come back). # Show My Work (Optional)? 3 35.C 6:15 PM Sunny 7/23/2022 1VA HW#15 Ch3.6 Implicit differential X Mathway | Algebra Problem Solve X + V X > C a webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762597_1 I K 2. [-/21 Points] DETAILS BERRAPCALCBR7 3.6.017.MI.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise For the equation, use implicit differentiation to find dy. dx 1 + 1 =3 X y Step 1 We want to find - by implicit differentiation. The derivative will be easier to find if we first rewrite the function as a sum of power functions. dx 1 +1 V : 3 Submit Skip (you cannot come back). # Show My Work (Optional) ? 35.C 6:15 PM Sunny 7/23/2022 1VA HW#15 Ch3.6 Implicit differential x Mathway | Algebra Problem Solve X + V X C a webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762597_1 K 3. [-/6 Points] DETAILS BERRAPCALCBR7 3.6.001. MY NOTES ASK YOUR TEACHER For the equation, use implicit differentiation to find dy dx y3 - x2 = 4 dy = dx Show My Work (Optional) @ 4. [-/6 Points] DETAILS BERRAPCALCBR7 3.6.005. MY NOTES ASK YOUR TEACHER For the equation, use implicit differentiation to find dy dx y4 - x3 = 4X dy = dx Show My Work (Optional) ? 2 35.C 6:15 PM Sunny 7/23/2022 1VA HW#15 Ch3.6 Implicit differential x Mathway | Algebra Problem Solv( X + X C a webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762597_1 K 5. [-/6 Points] DETAILS BERRAPCALCBR7 3.6.015. MY NOTES ASK YOUR TEACHER For the equation, use implicit differentiation to find dy dx y6 - 12 + y - 2 = x dy = dx Show My Work (Optional) 6. [-/6 Points] DETAILS BERRAPCALCBR7 3.6.041. MY NOTES ASK YOUR TEACHER A company's demand equation is x = v 500 - p2, where p is the price in dollars. Find dp/dx when p = 20. ap = dx Interpret your answer. O Changing the quantity will not affect price. O Prices increase by the absolute value of dp/dx for each increase of 1 in quantity. O Prices decrease by the absolute value of dp/dx for each increase of 1 in quantity. # Show My Work (Optional) ? 35.C 6:16 PM Sunny 7/23/2022 1VA HW#15 Ch3.6 Implicit differential x Mathway | Algebra Problem Solv( X + X C a webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762382_6 K 7. [-/15 Points] DETAILS BERRAPCALCBR7 3.6.045.MI.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A management consultant estimates that the number h of hours per day that employees will work and their daily pay of p dollars are related by the equation 90h + 18,000,000 = p3. Find _! at p = 300 and interpret your answer. Step 1 We want to find - by implicit differentiation and evaluate at the given point. To do so, we take the derivative of both sides of the equation, starting with the left hand side. Viewing h as a function of p, taking the derivative with respect to p, and recalling that we will get a - from the Chain Rule every time we take a derivative of h, we have the following. 90h5 + 18,000,000 = dh dp Submit Skip (you cannot come back) # Show My Work (Optional)? 3 35.C 6:16 PM Sunny 7/23/2022 1w. HWMS(h36lmpiitltdierentl3 x W MathwaylAIgebra Problem Sol x l + v 7 X ( $ C 0 webassign.net/web/Student/AssignmentiResp0nses/tutorial?dep:29238592&tags:autosave#question4762382_6 i3 W TO I l] o l H. [16 Points] BERRAPCALCBR7 3.6.065. ASK YOUR TEACHER The number of welfare cases in a city of population p is expected to be W : 0.006p4/3. If the population is growing by 1200 people per year, find the rate at which the number of welfare cases will be increasing when the population isp = 1,000,000. Show My Work (Optional) 0 9. [-16 Points] BERRAPCALCBR7 3.6.059.Ml. ASK YOUR TEACHER A large snowball is melting so that its radius is decreasing at the rate of 2 inches per hour. How fast is the volume decreasing at the moment when the radius is 3 inches? [Hint The volume of a sphere of radius r is V = $1113.] (Round your answer to the nearest integer.) Show My Work {Ominnall o VA HW#15 Ch3.6 Implicit differential X + V X C webassign.net/web/Student/Assignment-Responses/tutorial?dep=29238592&tags=autosave#question4762382_6 A large snowball is melting so that its radius is decreasing at the rate of 2 inches per hour. How fast is the volume decreasing at the moment when the radius is 3 inches? [Hint: The volume of a sphere of radius is V = mr3.] (Round your answer to the nearest integer.) in3 per hr Show My Work (Optional) 10. [-/6 Points] DETAILS BERRAPCALCBR7 3.6.043. MY NOTES ASK YOUR TEACHER The number x of MP3 music players that a store will sell and their price p (in dollars) are related by the equation 4x2 = 18,000 - p2. Find dx/dp at p = 120. [Hint: You will have to find the value of x by substituting the given value of p into the original equation. ] dx = dp Interpret your answer. O Sales will decrease by the absolute value of dx/dp for each $1 increase in price. O Sales will increase by the absolute value of dx/dp for each $1 increase in price. O Changing the price will not affect sales. # Show My Work (Optional) ? 35.C Sunny O W 6:16 PM 7/23/2022 1