You are taking a road trip in a car without A/C. The temperture in the car is 105 degrees F. You buy a cold pop at a gas station. Its initial temperature is 45 degrees F. The pop's temperature reaches 60 degrees F after 25 minutes.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 5t, where 0 ≤ t ≤ 1.5…

A: The answer as follows:

Q: Find the area A of the shaded region of the cardioid r = 9 - 9 cos (0) . 3 -X The cardioid (Express…

A: This is application of integration problem

Q: 1 Find the Taylor Series generated by f(x) = (7-X)⁹ at X=6 9 (7-x) 10 f'(x) = 90 f"(x) = (7-x)" f(x)…

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Q: Doint approximation. time (sec) 0 1 2 3 4 5 6 velocity (ft/sec) 26 47 49 30 7 2 19 feet

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Q: 1. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1).

A: Please see the below picture for detailed solution.

Q: Find the following limit. lim

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Q: 1.1: If y2 = x² + 2xy, then dy y+x dx a) y-x b) 2x + 2y x+1 c) y d) - x corre None of the above ||

A: Given y2=x2+2xy

Q: Let f(x) = f'(x) = f'(9) = 4log7 (x)

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Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8-7-6 -5 4 -3 13…

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Q: Find foda + C

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Q: O Use 1st and 2nd derivatives, sketch the graph of given function 2x x² - 1 f(x) =

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Q: Enter the exact answer. tan B FREE B 55 Figure 1 4

A: Please refer attached file for solution below

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: There were about 1.92 million Hispanic-owned businesses in 2001 and 2.42 million in 2003. a) Find an…

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Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

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Q: Evaluate the indefinite integral. 2x - 3 (2x² - 6x + 6)² dx + C

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Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

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Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: Question is solved.

Q: Find the radius of convergence for: (-1)"x" √n +7 n=1

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Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

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Q: 6) 3/2 · 4x²)³/; 9x dx

A: Our Aim is to solve the integral given below:-∫9-4x252x6dx -(i)

Q: A Law office has 20 files awaiting transcription. The legal secretary has been able to complete 2…

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

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Q: Consider the equations of two planes. x + y + z = 0, 8x - y + z-5=0 (a) Determine whether the planes…

A: This question can be solved using the concept of angle between two planes.

Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: 2. Use the process of implicit differentiation to find given that sin(4x) + sin(2y) =

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Q: Differentiate the following function. You do not need to simplify the derivative. F'(x) = F(x) = 6e²

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Q: Find the area of region A in the figure if the equation of the boudary is r = 4 cos (0). r=1 A A = X…

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Q: Find the future value at 5.25% interest, compounded continuously for 5 years, of the continuous…

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Q: Complete each statement below. The zero vector of Pg The set IS in the set because zero IS a…

A: Concept: A function that can be expressed as a polynomial is referred to as a polynomial function. A…

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of y=-x² + 7x between x = 1…

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Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

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Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A: Let's find volume by using triple integral.

Q: Convert x2+y2= 26 to an equation in polar coordinates in terms of ? and ?.

A: The given equation is x2+y2=26 we have to convert this equation into polar coordinate in terms of r…

Q: Evaluate £¹₁7 x8 − 7 x³ + 7 x² dx. Round your answer to two decimal places. £²₁7 r8 − 7 x³ +7 r² dr…

A: Given definite integral is: ∫-11(7x8-7x3+7x2) dx

Q: 76 6 27 6 Σ [5 (2 + (i - 1) =) * - 7 (2 + (x − 1))"] n n as a definite integral, that is provide a,…

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Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: (a) Find the critical numbers of the function f(x) = x(x - 2)5. X= (smallest value) X= X= (largest…

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Q: Use 1st and 2nd derivatives, sketch the graph of given function 2x x² - 1 f(x) =

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Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

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Q: The regions A, B, C, D, E, and F in the figure below are bounded by the graph of the function f and…

A: Topic -Definite integral In definite integral, Area below x-axis is considered as negative.

Q: 2- The circle ² + (y-2a)2 = 4a² is rotated about the line y = -1 where a > 0. A torus is obtained…

A: Given: the circle x2+(y-2a)2=4a2 is rotated about the line y= -1 then torus is obtained from this…

Q: 3. Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

A: At first we derive second order partial derivative of the given function   f(x,y)=yFxy.

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 5x e 5xy fxx (x,y)=…

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Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

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Q: 3. a. Solve the differential equation y'= 2x√/1-y² b. Explain why the initial value problem y'=…

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Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: Use the cross product u x v to find the obtuse angle between vectors u and v, where u = i +8j + k…

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