2. Newton's Law of Cooling An object that has been heated will cool to the temperature of the environment in which it is placed, such as the surrounding air or water. The temperature of the object at time can be modeled by the equation T(t) = T₁ + (To-T₂)e-kt for an appropriate value of k, where T = the temperature of the surrounding environment T = initial temperature of the object This model is called Newton's Law of Cooling. A hard-boiled egg at temperature 92° is placed in 20° water to cool. Five minutes later, the temperature of the egg is 45°. a) Use the given information to solve for k. b) Use Newton's Law of Cooling to determine when the temperature of the egg will be 30°. Round your answer to the nearest hundredth of a minute.

Q: Factor the following expression completely: 6X2 + X – 12

A: We will find the required.

Q: Prove the identity. 9 cos³x=(1-sin²x) 4 2 COS X

A:

Q: Find the average rate of change of the function f(x) = Average rate of change = Give exact answer!…

A:

Q: Question 2 Solve the following simultaneous equations xy = 256, 3log, (v) = 1 (4 marks)

A: Using logarithmic property Logxy=z then apply exponant both side we get y=xz

Q: 04 * O O Evaluate -1+2x-2x^2 -1+2x+2x^2 -1-2x-2x^2 -1-2x+2x^2 d dx 1-x fe 1² dt).

A:

Q: 5. To find the -intercepts, set x equal to 0.

A: Intercepts are those points where the graph of a function intersect the axis

Q: If it takes someone t minutes to drive, run, or walk a mile, then their average speed s(t), in miles…

A: We will put the value of t to find s(t)

Q: For the function f(x) 1 42 P 2, find the value of x for which f(x) = x.

A: Equate f(x) to x for finding x

Q: Distance (km) d 100 80 60 40 20 Distance traveled by car according to time B OA 0A 1 C D E F 2 2 3 4…

A: As per the given Graph    We need to find the average rate of change for each of the letters…

Q: A painting is purchased as an investment for $175. If its value increases continuously so that it…

A: A painting is purchased as an investment for $175.If its value increases continuously so that it…

Q: 1. (a) By reading values from the given graph of f, use five rectangles to find a lower estimate and…

A:

Q: (b) d'y dx² dy_9y=2x+4 dx d'y dx² dx -+10y=x² +2 dy

A:

Q: Write the end behavior for the graph

A: NOTE: Refresh your page if you can't see any equations. . from the graph, we can write the end…

Q: Find the equation of the sphere if one of its diameters has endpoints (6, 4, -7) and (8, 8, -1)…

A:

Q: What is the slope of the tangent line to x² cos² y sin y = 0 at the point (0, π)? - 0 -2πT 27²-1 O-1…

A:

Q: Rewrite sin (2 sin ¹4v) as an algebraic expression in v.

A:

Q: 2. Given: y = 4 sin applifude b. period C. phose chift ditumine;

A:

Q: ere are two possible values for cos. Find both. is known that tanis negative, then only one of the…

A: we will  find the required.

Q: 22.) lim x2 cos³ x 1-sin² x

A:

Q: How do you find this using a graphing calculator?

A: Let's find local minimum by using graphing calculator.

Q: Find sin 2x, cos 2x, and tan 2x if sin x = √5 and x terminates in quadrant

A:

Q: 14. A rectangular garden is to be planted against the side of a barn. The gardener has 80 metres of…

A:

Q: Use the 2 solutions Bernoulli's equation dy y + = x²y² dx x

A:

Q: 7. G(x) is decreasing over (-∞, 4) and (9, ∞) and increasing over (4, 9).

A:

Q: Find f (0) and find x when f(x) = 0 for the following function -5 10 5 0 -5

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Calculate the derivative. y = cosh-¹(11x) (Use symbolic notation and fractions where needed.) dy dx

A:

Q: 1. The sum of the first five terms of the sequence n+ in simplest form is

A:

Q: Find an equation of a sphere if one of its diameters has endpoints  (1, 4, 6) and (3, 8, 8).

A: Here we have to find the equation of a sphere.

Q: Osts $2.50 to make each shirt. hat do you think the independent variable What do you think the…

A: Topic:- application of algebra

Q: ( 1 Suppose we define a function Blue as follows Blue (s) = 5s²+1. Steven is asked to find Blue…

A:

Q: Find the directional derivative of the function f (x, y) = xe 2y at the point (1, 0) in the…

A:

Q: ify the correct way 000(10^-6) N*m N*mm mN * m 100 3) *

A: topic :- algebra

Q: For the given position vectors r(t), compute the (tangent) velocity vector r' (t) for the given…

A:

Q: Given that f(x)=√√x²-4 and g(x)=√√√4-2², what is the domain of f(x)+g(x)? OR O [-2,2] O {-2,2} None…

A:

Q: Which of these is an equation of the tangent line to the curve (+2+ 2t + 3,4t cost, 2 e³t) at the…

A: Please see the below picture for detailed solution.

Q: Find an equation of the plane that passes through the point P(−4, −8,7) and has the vector n = (-4,…

A:

Q: Write the integral as a sum of integrals without absolute values and then evaluate. 9 = √√₁²₁1x² -…

A:

Q: page-2 15 -- :∴I 1 = { " ( 2²²-22²"+2") (-42) X //똥 = 13 = p(222 = = 16 14 Z = [루* - 2. " + Z 16 14…

A:

Q: Find the unit tangent vector at the indicated point of the vector function T(A/2) = ( r(t) = et…

A: Given vector r( t ) = e6tcost i + e6tsint j + e6t  k

Q: 3. Consider the functions f: R → R defined by f(0) = 4 + sin 0 and g: R → R defined by g(0) = sin…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Let the graph below represent f(x) on the interval [−2, 2]. For which values of x is ƒ'(x) = 0? 3

A: We know that the function has derivative 0 at the bumps. So, from the given graph, f'(x)=0 will be…

Q: how did you get 36-63+28/504

A:

Q: If 5e^xy−2x=y+10.6, then the rate of change of the curve at the point (1,1) is __

A:

Q: the logistic equation (with t in months.) P(t) = 0.0225P(t)- 0.0003P(t)² ) Find out the percentage…

A:

Q: Find parametric equations for line that is tangent to the curve x = cost, y = sin t, z = t at the…

A:

Q: Consider the curve given by x² – 6y² – 5 – 4xy . x+2y dy dx 2(3y-x) Show that

A: Given : x2-y2=5-4xy   To Show : dydx=x+2y2(3y-x)

Q: If f(x) = 2 + Find f'(5). 68 + 2 find ƒ'(x). x²²

A:

Q: Consider the curve y = 5x3. The sketch of the portion of this curve between x = -1 and x = 8 is…

A:

Q: The vector w = ai + bj is perpendicular to the line ax + by = c and parallel to the line bx - ay =…

A:

Q: Use the information given below to find cos (a −ß). 8 17' 3 tan B with B in quadrant III 4 sin a =…

A: