When a bowl of hot soup is left in a room, the soup eventually cools down to room temperature. The temperature 7 of the soup is a function of time t. The table below gives the temperature (in °F) of a bowl of soup t minutes after it was set on the table. t (min) T (°F) t (min) T (°F) 0 251 35 106 5 225 40 95 10 200 50 86 15 177 60 79 20 155 90 73 25 30 136 118 Find the average rate of change of the temperature of the soup over the first 20 minutes and over the next 20 minutes. 120 150 70 70 first 20 minutes next 20 minutes °F/min °F/min During which interval did the soup cool off more quickly? the first 20 minutes the second 20 minutes neither

Q: dy Find dx x=8e8 y = e 010

A:

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 32+ y² = 5. maximum value =…

A:

Q: d 3 Evaluate dx √√In(6 - x²) at x = 1.

A: −15ln(5)32​2​Explanation:

Q: How Hey Find Find the largest product the positive numbers X, Y and Z can have if x+y+z² = 16,…

A: Let  Let

Q: 2 Find the point on the sphere x²+ y²+z²=4 farthest from the point (1,-1,1)? ans.i- 2 (금) v i

A: Let the point  on the sphere which at largest distance from the point By using distance formula Let…

Q: The value of a car, V = f(a), in thousands of dollars, is a function of the age of the car, a, in…

A: Detailed solution of the problem is attached below.Explanation: Detailed explanation:

Q: If f(x) = 7 sin(2x) arcsin(x), find ƒ'(x).

A: f′(x)=14cos(2x)arcsin(x)+1−x2​7sin(2x)​Explanation:Given function is  f(x)=7sin(2x)arcsin(x) We need…

Q: Let f(x)=3x³-5x²-2, x≥ 1.5. Find the value of df at the point x=248 = f(5). dx df The value of dx 1…

A:

Q: A. Find the equations of the intersection line between the planes 3xyz2 and x-y+2z = 3

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A: The required answer is 24Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find the slope of the tangent line to the curve below at the point (7,7 4x+3y+ √3xy =…

A:

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: √x(t) = −3+² -…

A: Therefore, the required answer is x=16−3​y2+89​y−1627​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A:

Q: The function f(x) - 244 is concave down on which interval?

A: Given: To Find: To determine the interval on which the above function is concave down.

Q: Chow is it called, #8 Given the surface x²+ y² = Z² Sketch in 2D the level curve 4 corresponding to…

A: The surface x² + (y²/4)= (z²/9) is an elliptic paraboloid.The level curve for z=12 is an ellipse…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The problem involves finding the dimensions of a lidless square-based box with a volume of 4000 cm³…

Q: Find all solutions of the equation in the interval [0, 2π). tan 20+2 sec0=-1 Write your answer in…

A:

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

A: The given total inventory cost function

Q: I+t #1 Let r(t)=(x(t), y(t), z(t)) = (1-{², t- ½, ±). (a) Find the moment of time to and the point…

A: Image attached.Explanation:a)  b)

Q: use the ratio test to determine the convergence or divergence of the series: the sum from n = 0 to n…

A: The series     ∑n=0∞​3n+14n​   diverges.     Explanation:Detailed explanation:To determine the…

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: The required value of directional derivative is 2.3 ( in decimal). In fraction: Directional…

Q: Solve the given integral equation or integro-differential equation for y(t). y' (t) +27 (t-v)y(v)…

A: The objective of the question is to solve the given integro-differential equation for y(t). The…

Q: C(q)=560+ 15g, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars…

A:

Q: 7) The region bounded by y= √x, y= 2, x=0 is revolved about the y-axis to generate a solid, its…

A: The objective of this question is to find the volume of the solid generated when the region bounded…

Q: Find d³y/dx³. y(x) 2STENTOR x(x-1) 3

A:

Q: base of a solid is bound by y=9x, y=36 and x=0 find the volume of the cross-section rectangle…

A: V=4032 cu. unitsExplanation:Given the equation of the base,y=9xy=36x=0  Solving for the volume of…

Q: In this problem, p is in dollars and x is the number of units. Find the producer's surplus at market…

A: Part 1: AnswerThe producer's surplus at market equilibrium for the given product is approximately…

Q: Use the table of values of f(0) = cos (40) 0 to estimate lim f(x), if it exists. 0-0 0 -0.1 -0.01…

A: From the definition of limit, limit does not exist when the left hand limit and right hand limit is…

Q: Let y = tan(3x+5). Find the differential dy when x = 1 and da = 0.2 0.61185103 Find the differential…

A: Let .To find the differential .To find the differential .

Q: Find the absolute extrema of f(x) = 7x2 x-5 on the interval [-1, 2]. maximum, f ; minimum, f

A: on the interval Note:As per bartleby guidelines we are supposed to answer only3 sub-parts (if there…

Q: 6. Sketch an even continuous function with all of the following features: • Absolute minimum at -5 •…

A: Function is even continuous  function.  Absolute minimal at -5 Zeroes at 4 and -4y- intercept at -23…

Q: 5. Find the indicated partial derivative(s). (a) f(x, y) = x4y² - x³y; faxx, fxyx

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: A.…

Q: The daily cost C (in dollars) for a manufacturer to produce a electronic video components is given…

A: An increase of $ 5600/191Explanation:

Q: Əz Əz and at Use the chain rule to find as || 8」8 z = tan (#). u = 7s + 9t, v = 9s - 7t

A: answers are given below.Explanation:

Q: * x f(x) f'(x) 1 3 1 2 -1 3 3 3 3 5 -2 4 -2 4 5 4 -2 The table above gives values of f and its…

A: a)we can estimate the value of f'(1.5) to be 1.b)Why must there be a value c for 1<c<3 for…

Q: dy dx = dy 33 dx = y = ln 3x14 +1 y = x cos(x)

A: The solution and explanation of the given problem are attached below.Explanation:Step 1:

Q: Find equations of the following. x² - 2y²+ x² + y = 5, (5,3,-2) (a) the tangent plane (b) the normal…

A: Please refer below page.If you have any doubts please feel free to ask.Explanation:Step 1: Step 2:

Q: Use the linear approximation to estimate (3.03)³ (1.03)³ ≈

A:

Q: When the cross product between any two vector is zero then these vectors are perpendicular Ignore…

A: Give statement "When the cross product between any two vectors is zero then these vectors are…

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A: Answer :(a)  62   (b)  423​Explanation:For any query please ask in the comment box.

Q: For the function f(x)-4+ 12x²-x³, find the local extrema. Then, classify the local extrema using the…

A:

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Global maximum at (2.5, 5) of 31 Global minimum at (0, 0) of 21Explanation: Given that, maximum : In…

Q: y= log(ln(2x)) , and explain why there is no y-intercept.  (an explanation of the problem and how to…

A: No y-intercept Explanation:

Q: Evaluate the following integrals using partial fraction decomposition, when applicable

A: 2x2​+3x−3ln(x)​+328ln(x−3)​Explanation:

Q: 2 sin x+3sx=3 Write your answer in radians in terms of π. If there is more than he solution,…

A: c

Q: For the given cost function C(x) = 44100 + 300x + x2 x², First, find the average cost function. Use…

A:

Q: Can you do part (b) ?

A: The solution is given below please refer to the solution  and if you have any doubt with regards to…

Q: Problem #3: Consider the following function. f(x, y) = 2x3+24xy-12y2 (a) Find the critical points of…

A: Refer explanationExplanation:

Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…