An object that is heated by a manufacturing process to 90°C is placed into the surrounding air which is 28°C. 30 minutes after being removed from the heater, the temperature of the object is 65°C. Round your answers to 3 decimal places. a. Find a function that gives the temperature of the object at any time, t, in minutes after removal from the heater. P(t) b. Find the temperature of the object 45 minutes after it is removed form the heater. P (45) = °C

Q: Use Wallis's Formulas to evaluate the integral. π/2 cos(x) dx 0

A:

Q: csch-1 x= x = sinh sinh11 X Prove mathematically that the right-hand side is equal to the left-hand…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Exercise 2.6 Find derivatives of the following functions: i. y = ln(x²+2x+3) iii. f (t) = 1 e2t ==…

A: Step 1: For y=ln(x2+2x+3): Identify the function: y=ln(u), where u=x2+2x+3. Apply the chain rule:…

Q: Hello, how do I simplify factorials? For example: n!/(n+100)!

A: We can simplify the factorial by expanding the  and canceling the common terms:  lets simplify the…

Q: Use cylindrical coordinates. Evaluate 2 [S] √x² + y² dV, where E is the region that lies inside the…

A:

Q: Solutions to question 4 please

A: Step 1:Step 2:Step 3:

Q: Find lim cos 8+19 x Enter INF for ∞, -INF for -∞o, and DNE if the limit does not exist. Answer:…

A: Step 1: Step 2: Step 3: Step 4:

Q: MAT441 CALCULUS II - PROJECT #3 Exercise 4 dy dx Given that y sinh (x2))cos(x). Find Answer. Step 1:…

A: In case of any doubt Please ask in comment section

Q: Please see image

A:

Q: Let f(x) = 4x. (a) Sketch the region R under the graph of f on the interval [0,2]. 1 2 3 Find its…

A: (a) To sketch the region R under the graph of f(x) = 4x on the interval [0, 2], we'll draw the line…

Q: Find the cross product (i+e¹j+e¯¹k) × (5i + etj − e−k).

A: Step 1:Here need cross product of ,(i+etj+e−tk)×(5i+etj−e−tk) If a=ai+bj+ck and b=xi+yj+zk given…

Q: What percent of the student were using train

A: Step 1:

Q: dx 1) f 4) S cosh (lnx)dx x 2)S 18 tan²x secx dx (2+tan³x)2 2 dx 3) (1+x²)tan-1 x * 5) f sec¯¹ √x dx…

A:

Q: 4. 5

A: If you have any problem let me know here in comment box for this thankyou for your question.

Q: Use the following equations to answer the questions below: ⚫ Volume of a parametric curve revolved…

A: Here's the process of using the given formula to find the volume of a solid of revolution when a…

Q: Find the open intervals where f (m) is concave up and where it is concave down. Enter the intervals…

A:

Q: *Use first derivative test

A: Step 1: Step 2: Step 3: Step 4:

Q: Homework

A: {if you have any queries please feel free to ask..}

Q: For these questions use the first derivative process to show the second part of the AST condition…

A: (a)Step 1: Given : ∑0∞​k2+1(−1)kk​ Verifying the conditions of 1st derivative test- Step 2: Now…

Q: 7) Two residential buildings are to be constructed with a grassy recreational area between them. The…

A: The solution has been attached below:

Q: 3. h(2) = re* (a) Determine the domain (b) Determine if the graph has any asymptotes, or any kind(s)…

A:

Q: Find the derivative of y y=x" Option 1 Option 2 π.χ Π x" Inx

A: To find the derivative of y = xπ, you can use the power rule for differentiation.The power rule…

Q: Consider two functions f and g on [2,9] such that √ f(x)dx = 11, √ g(x)dx = 7, √ f(x)dx = 4, and √…

A:

Q: 2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at…

A: In the scenario described, the rat's movement through the maze resembles a random walk, where at…

Q: Evaluate the indefinite integral. cos(x) 8 sin(x) + 40 dx

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 4. 8

A: Let's assume t=e4x−4x, which implies dt=4(e4x−1)dx.So, our integral becomes:41​∫t2dtNow, integrating…

Q: 21

A: Please comment down for any doubt. If my answer helped you please do rate helpful.

Q: 6. Evaluate the given definite integral using the fundamental theorem of calculus. 1 (a). Sex (4…

A: Step 1: Step 2: Step 3: Step 4:

Q: On a hot summer afternoon, a city's electricity consumption is -3+² + 18t+ 10 units per hour, where…

A: To find the total consumption of electricity between 1 p.m. and 4 p.m., we need to integrate the…

Q: Solve the triangle. B = ° (Do not round until the final answer. Then round to the nearest degree as…

A: Solution-

Q: Find the area of the surface generated by revolving the curve y = √√/85-x, 36≤ x ≤ 49, about the…

A:

Q: Given the following points: A (4, -2, 0) and B (-2, -4, 2), find: 1. The length of the segment AB…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Use the Fundamental Theorem of Calculus to find 8 cos() da

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Homework

A:

Q: 16

A: Step 1:

Q: Solve this problem and provide a detailed explanation with full mathematical steps and reasoning…

A: 1. 2. 3. 4.

Q: Find the area of the region. interior of r² = 36 cos(20)

A: Step 1: put r=0 and calculation of angle  Step 2: Angle Q  Step 3: put the limit of integration…

Q: Q5

A: 1. First, we look at what's under the line in the integral2. We make it simpler by changing it into…

Q: Use the washer method to find the volume when the region between y = x² and y=x+2 is revolved around…

A:

Q: Use the disk method to find the volume when the region between y = x, x = 0, and y = 1 is rotated…

A:

Q: x+2x-1 We want to compute (2-2)2 d. (x²-x-2)2

A:

Q: Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for…

A: A = P(1 + r/n)^(nt)where:A = accumulated amountP = principal amountr = interest rate per yeart =…

Q: At the end of an advertising campaign, weekly sales declined according to the equation y= 14,000…

A: Given,y = 14000(5-0.06x), where, x is the number of the weeks after the end of th campaigna)sales at…

Q: sech¹ x = cosh X Prove mathematically that the right-hand side is equal to the left-hand side for…

A: Step 1: Step 2: Step 3: Step 4:

Q: 5. Determine the end behavior of the given functions. lim f(x)= lim f(x)= 2-90

A: We can see clearly   from the graph       as   x is approaches   to  toward   2 from RHS     the…

Q: Consider the power series: n=1 (x+4) n 7n√n Find the Interval and the Radius of Convergence. Show…

A: Step 1:​S=n=1∑∞​7nn​(x+4)n​​Step 2:​Using the Ratio TestFor the Ratio Test, we consider the limit:…

Q: Use the disk method to find the volume when the region between x = y = 4, y = 0, and x = 0 is…

A:

Q: 3. Set up iterated integrals for both orders of integration. Then evaluate the double integral using…

A: Step 1: Step 2: Step 3: Step 4:

Q: Can you please solve this integral with a step by step explanation?

A: Step 1: Step 2: Step 3: Step 4:

Q: The contour plot below shows the elevation in feet above sea level of a mountain in West Virginia.…

A: Sure, I can help you with that. The question asks you to set up and evaluate a Riemann sum to…