Express the number as a ratio of integers. 1.325 1.325325325.... -

Q: = sin (5√) at the point (7²,0). Enclose numerators and denominators in parentheses. For example, (a…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…

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Q: Tutorial Exercise Consider the differential equation x²6xy +10y=0; x², x5, (0,00). Verify that the…

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Q: Question 18 -6 -5 -4 -3 -2 -1 8+ (2) 7 65 4 32 My 1 -1 -2 -3 --4- ✓ to t 1 3 Find an equation for…

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Q: 1. Determine whether the following series diverge or state that the Divergence Test is inconclusive.…

A: ∑k=0∞ kk+1

Q: The function h(t) = ... gives the height from the ground of a ball thrown upwards. The time t is in…

A: We have to find the height when the ball is thrown, initial velocity, the average rate of change at…

Q: Find the following integrals. Do not add any constants of integration, as the resulting functions…

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Q: Solve the differential equation by variation of parameters. 1 4 + ex y" + 3y' + 2y = 4

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Q: find X so that the net present worth of the investment is zero

A: answer is given in step2

Q: 9 (4) Giver Sifon dx = 37 g(x) dx = 16 So Find S (2 f5r1 + 3 ger)) f(x) dx and

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Q: Evaluate the integral. 6 1 (x² - 1)3/2 2 (x²

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Q: Evaluate I= I=S 2+41 Iti NJ Z 2 dz

A: This question is related to definite integration, we will solve it using given information.

Q: You want to buy a $243,000 home. You plan to pay 10% as a down payment, and take out a loan with a…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: Let X 1 f(x) = √²/² 0 e²x² 842 dt. t4 +5 ex none of the choices e2x Find the derivative f'(x).

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Q: Consider the following. u = (-10, 0, 8) v = (5, -9, 0) Find u x v. Determine if u x v is orthogonal…

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Q: Find the general solution of the given second-order differential equation. 25y" - 15y' - 4y = 0…

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Q: At the beginning of an experiment, a scientist has 160 grams of radioactive goo. After 90 minutes,…

A: topic- exponential function

Q: Find the average value of the function over the given solid. The average value of a continuous…

A: Average value of the function = 1V ∫∫∫E f(x,y,z) dzdydx .

Q: Calculate the exact slope m (rather than a decimal approximation) of the straight line through the…

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Q: Solve the following inequality. (x+5)(x+3)(x-7) <0

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Q: Find the general solution of the given second-order differential equation. 20y" 11y' 3y = 0 y(x) =

A: The given differential equation is: 20y''-11y'-3y=0   So, we can also write as; 20D2-11D-3y=0 The…

Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: A large snowball is melting so that its radius is decreasing at the rate of 4 inches per hour. How…

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Q: HOW DID HE GET THE VALUE INSIDE THE CIRCLE cos² x D²+1 For given particular integral multiplying and…

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Q: The masses m, are located at the points P. Find the center of mass of the system. = 2, m3 4, m2 6.…

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Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Find the area between the curves. 6/5 y=x, y = 4x 1/5 ... The area between the curves is (Do not…

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: Let f be the piecewise function i. 11. f(x) = (x³ + 6x² + 8x x + 2 x 1 Sketch the graph of f. Based…

A: Solution is given below:

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

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Q: We have verified that x² and x are linearly independent solutions of the following second-order,…

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Q: Let f g and h be the functions defined below i. 11. f(x) = 5¹ = 10x₁ (²² = 4) g(x) = log5 h(x) = 6 x…

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Q: Find the equation of the tangent line to the curve at the given point using implicit…

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Q: Find the (a) derivative y'= dy dx y = (n² + 5 secx) ㅠ of following Question tog 3 x

A: Note: Due to guidelines i can solve only your first question. Solution: a) y=πe+5sec xlog3x…

Q: and the partial fraction decomposition. -2x-9 2 x -3x -2x - 9 2 X - 3x - SERT 0

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Q: Determine the general solution of the given differential equation. y"" - y = 11 sint NOTE: Use C₁,…

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Q: Find the radius of convergence, R, for the power series ₁ (−1)n. in=. O R = 0 R = 2/1/2 R = ∞ R = 2…

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Q: Determine the region R in the xy-plane that minimizes the value of JJ (x² + y² - 8) dA. OR={(x, y):…

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…

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Q: Given that calculate f'(-1). f(x) h(-1) h'(-1) = || || x¹¹h(x) 3 6,

A: Given, f(x)=x11h(x)h(-1)=3h'(-1)=6

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

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Q: Use Newton's method with the specified initial approximation x₁ to find x3, the third approximation…

A: Given equation:- x5-x-5=0 , x1=1

Q: Let the function be f(x)=-log(base3)X. Use the properties of the reciprocal of a function to graph…

A: We have to find the reciprocal of given function.

Q: d) Consider f(t) = bt, where t&R and b ER such that 0 by [Select] e) 5 log25 k² = k where k denotes…

A: To label the following statements as T for true or F for false.d Consider ft=bt, where t∈R and b∈R…

Q: 8²f Let f(x, y) = cos(xe¹²) + cos(x + ey²), find əxəy O a. O b. O C. O d. -2yey² (sin(xe¹²) - x…

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Q: ep 2 We have found that the roots of the auxiliary equation are m₁ = -1 and m₂ = -2. In the case…

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