area given by the following.   A = 1/2xy   If the rate of change of x is 2 units per minute and the rate of change of y is 5 units per minute, find the rate of change of the area (in units2/min) when x = 8 and y = 5

Q: Differentiate the function. g(t) =2t -3/4

A: Given information: The expression is g(t) =2t -3/4 Calculation: Use the power rule of differentiatio...

Q: #31 2D

A: Given data: The first parametric equation is x=x1+(x2-x1)t. The second parametric equation is y=y1+(...

Q: Let a> 1 be a constant and let R be the region bounded by y = 10x² and y = 10x + 20 . Find the volum...

A:

Q: Let a be a constant. Given that –104 3x² In(ax)dx = e15 ( 40 – –, find In a. 3

A:

Q: Let a be a constant. Given that 3x2 In(ax)dr = e15 ( 40 -104 + find In a. 3

A: Solving by definite integral we have

Q: answer B

A:

Q: Solve the logarithmic equation 6 ln(2x) = 30. Be sure to reject any value of x that is not in the do...

A: To Solve: 6ln2x=30 Concept: elnx=x

Q: Find and simplify the difference quotient [f(x + h) - f(x)]/h, h ≠ 0 for the given function : f(x) =...

A: Consider the given function f(x) and find the value for f(x+h). fx=3x2+x+5fx+h=3x+h2+x+h+5=3x2+h2+2x...

Q: The area of a trapezoid is given by A = h(b1 + b2). Use the formula to find the height of a trapezoi...

A: Given data: The given area of the trapezium is A=135. The first parallel length is b1=15. The second...

Q: Integrate  (tanx+cotx)2

A: Integrate    (tanx+cotx)2

Q: Let a be a constant. Evaluate L (* +2² + a) sin(8=") + 9=*)dz. -2

A: It is given that I=∫-22x4+x2+asin9x3+9x2dx Re-writing the given integration as I=∫-22x4sin9x3 dx+∫-2...

Q: Just the right choice

A: We are answering only the first question as per our honor code. If f(x)=2x2-ax-4 and the equation of...

Q: Let a be a constant. Evaluate ((x* + a? + a) sin(10r) + 9a)dr.

A:

Q: Let r(t) = ⟨1, 2t, 3t2⟩. Compute∫r(t) dt.

A: We have given vector r→t=i^+2tj^+3t2k^ Then, ∫r→tdt=∫i+2tj^+3t2k^dt=∫idt+∫2tj^dt+3t2k^dt=t+c1i+2t22+...

Q: Suppose that a continuous function g satisfies: | = 36 and g(x)dx | 9(2x)dr = 15. 0. : = =p(= | z9(3...

A:

Q: define method of undetermined coefficients ?

A: in the non-homogeneous ordinary differential equation and recurrence relations, this method is used ...

Q: 3) Find the area of the region enclosed by the following curves. y = x² and y = -x² + 8x + 10 %3D

A:

Q: Use the graph of the function to identify its domain and its range.

A: Given graph of the function is: Domain is the set of possible input values. Domain of the graph is ...

Q: Please Answer

A:

Q: If f(x) = –3x + sin(47x) for x E [0, 1], find the smallest value of c E (0, 1) which satisfies the m...

A: The Mean Value theorem states that for a continuous and differentiable function f(x) on the interval...

Q: Calculate the derivative of the functions given below. a) f (x) = 2x + 1                3x − 1 b) f ...

A: We are authorized to answer the three subparts at a time, since you have not mentioned which part yo...

Q: Let a > 12 be a constant. Evaluate 4x + 32x + 40 +2a dr (4x + a)(x + 6z + 10)

A:

Q: The exponential models describe the population of the indicated country, A, in millions, t years aft...

A:

Q: Given the graph of y = f(x), as shown: 1. What is the domain of f(x)?    2. What is the range of f(x...

A: Given,  

Q: Solve the given triangle. Round lengths of sides to the nearest tenth and angle measures to the near...

A: We know that the sum of angle of a triangle is 180 degrees. Therefore,  ∠A+∠B+∠C=180∘42∘+96∘+∠B=180∘...

Q: Simplify the radical expression, if possible : 3√150

A: Given information: The radical expression is 1503. Calculation: 1503=5×5×3×23 It can be seen from th...

Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and | 9(20)dx = 12. Find æg(3x²)dx.

A:

Q: Set a decimal is an order from least to greatest

A: Solution: The objective is to find how much flour and sugar does the recipe use altogether.

Q: S* 16sin(t")dt Evaluate the limit lim

A:

Q: If y = (x + sin(x – e))™ª then what is the value of y'(e)? а) — з b) 3 с) — 2 d) 2 e) – 1 - -

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Q: Let a > 1 be a constant and y(x) = (12e- sin z – 4) In(x+a). Find y'(0). Türkçe: a > 1 sabit olmak ü...

A:

Q: Use the graph of the rational function in the given figure (see attached) to complete the statement:...

A: We can  see from the graph when x→-∞ graph of function tends to zero i.e fx→0

Q: Find the general solution of the system below. xi = x1 + x2 x2 = 4x1 + x2

A:

Q: 2,50 Puanlar) 22 - 4 Which of the following is FALSE for the graph of the function f(a) = I +1 a)y =...

A:   Proper graph is :

Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

A:

Q: Solve the initial value problems dr/dθ = cos πθ, r(0) = 1

A:

Q: If f(x) = –3x + sin(47x) for x E [0,1], find the smallest value of c E (0,1) which %3D satisfies the...

A: The given function is, fx=-3x+sin4πx Then, f'x=-3+4πcos4πx Consider for x=0 fx=0f(1)=-3 Then, f(1)-f...

Q: Find the products: a. 4i(3 - 5i)    b. (7 - 3i)(-2 - 5i).

A: The given expression is 4i3-5i   4i3-5i=12i-20i2=12i+20        i2=-1=20+12i

Q: For each stated limit, find the largest possible δ-neighborhoodthat is a proper response to the give...

A: Concept used: The limit of the function f(x) is L when x approaches  x0 where f(x) is defined on ope...

Q: A hotel has 200 rooms. Those with kitchen facilities rent for $100 per night and those without kitch...

A: Lets assume x represents the number of rooms with kitchen facilities. And y represents the number of...

Q: Let A be a positive real number. If the absolute minimum value of f(x) Ar5 35x on [0, oo) occurs at ...

A: If the absolute minimum value of f(x)=Ax5-35x3 on [0,∞) occurs at x=cAk. Where A be a positive real ...

Q: Find the domain and range of the function. f(x) = x3

A: the given function is: fx=x3 we have to find the domain and range of the given function.   as we kno...

Q: Suppose f is an odd continuous function whose mean value (with respect to integral) on the interval ...

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Q: Find (1 + i)8 using DeMoivre’s Theorem. Write the answer in rectangular form,a + bi.

A:

Q: Find the derivative of the function. f(t) = (6t + 3)2/3 f '(t) =

A: Given function, f(t) = (6t + 3)2/3 we have to find derivative of the given funcction.

Q: Please help me

A: Since you've posted multiple questions, we solve the first question for you. If you want to be solve...

Q: Evaluate the following limits using limit laws.

A: Given limit is limt→-2t2-1t2+3t-1.

Q: If f(x) = 2x? (a, b) is y = -4 and the equation of thenormal line to the curve at the point ax + c f...

A: The given curve is  f(x) = 2x2 - ax - 4..... (1) Equation of normal line on the given curve at (a, b...

Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

A:

Q: How much additional spending will be generated by a $10 billion tax rebate if 60% of all income is s...

A: Given, Annual payroll is 10 million$ Rate of spending is 60% We have to find additional spending. wh...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.