A force of 750 lbs stretches a spring 3 inches from its natural length of 15 inches. The work done in stretching the spring from 3 inches to 6 inches is: a 2250 in-lb b. 4500 in-lb 1125 in-lb d. 3375 in-lb C.

Q: A diabetes test is positive 85% of the time when the patient has diabetes and negative 95% of the…

A: Given data:- Diabetes test is positive 85% of the time when the patient has diabetes  diabetes test…

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A: Given: The depth function: D(t) = 2sinπ4t+5π4+5 Depth is changing at 6 a.m. t = 6

Q: 19. 2x³y = y(y² + 3x²).

A:

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

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A: Here is the solution:

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Q: R If is in standard position and ≤0≤ and sin 2 O 5 O_3 3 3 9 then the value of tan is:

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Q: y = ln(4x³ + 7x)

A:

Q: -10 -5 f(x) 10 10 5 10

A: Note: Since the student has posted 2 sub-parts of the question in which the part (1) is complete and…

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Q: Consider the rational function f(x) = x²-x-6 x²+3x (i) Factorise the numerator and denominator. (ii)…

A: As per guidelines, we must answer only three of the subparts of a question given. So, I answer the…

Q: A1. SOLVE STEP BY STEP IN DIGITAL FORMAT Using the following function and the given intervals…

A: Given - f(x) = 4x^2 - 6                [ 3 , 6 ] ∆y/∆t =[ f(X2) - f(X1) ] / ( x2 - X1)

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A: Given that The Bus A leaves at 8:00 with speed of 50 km/hand bus B leaves at 10:00 with 70 km/hSo,…

Q: 15 Lo - - dx 15 X (x + 1) ²/ O 0 O or| 800 88 O 1 O 176 5

A: The answer is 0.

Q: Given the function y = −2x√/2 - 4x, find dy in any form.

A:

Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

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Q: dv/du = (u — v)² — 2(u - v) - 2.

A: Here, the given DE is: dvdu=(u-v)2-2(u-v)-2...(1) Substitute u-v=p differentiating it with respect…

Q: 3 2 -1 2 we rational function f(x) = 1 3 Q 20 2.5r2 +4 > identify the int

A: Topic:- calculus       Definition:- If the second derivative of a function is negative on some…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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Q: ΣΠ n=1 a. 1+4+1 6n 61 5 b. 41 5 is equal to c. The series diverges. d. 66 5

A:

Q: ex 1₁-0² (1 - e²x) a. 3 b. C. ex VI d. √1 G ex ex 3 2 5 ² ( + 2 1-e(2x) 2 5 dx e2x In 1-e2|+C e2 + C…

A:

Q: On the line y = 2x + 1, what value of Δy corresponds to Δx = 3? Δy =

A: y=2x+1 We have to find ∆y corresponding to ∆x=3.

Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: 2 6) Compute the area bounded by y² + 2y + 4 and y = 4.

A:

Q: (-1,1) a N (1,1) 2

A: find the domain and range of the given graph Domain: set of x values for given function Range : set…

Q: Use summation properties and formulas to rewrite and evaluate the sum. 31 Σ [(3i)² – 6i] - i=1

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Q: Answer all of the questions below about the function f(x) graphed below when x = 5. 8 8 f -10…

A: Given Graph:-

Q: 1. The graph of y=f(x) is given below. -4 2 2 -2 a) Find lim f(x) or state why it does not exist. 7…

A: Given

Q: An internet bookstore charges $15 shipping for orders under $100 but provides free shipping $100 or…

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Q: dr Let A be the area of a circle with radius r. If dt = 4, find dA dt when r = 5.

A: Area of a Circle , A = πr2 ; where, 'r' is the radius of the circle .

Q: (4) (d) 2-7 dx 4x-2 x²-1 (4) (e) S 7x (4x²+5)3 dx

A:

Q: A y 10+ -10-8 -6-4 -2 8 9 2 2 7 6 8 -10- 2 45 8~9 10 X

A:

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

A:

Q: Determine the exact solutions to cos: O ○ 0=160=² ○ 0-5,0- 7x 0= 6 6 O O 0 7x 6 5x 6 R 0= =,0= 6 11x…

A: We can answer the question in the following steps.

Q: y=x4Inx

A: Topic = Derivative

Q: For the following equation, find Answer: dy da || y = -4x5 8x³ + x² +9x

A:

Q: Find the Domain and Range of the function (Have your answers in interval notation)

A: Question: Find the Domain and Range of the function (Have your answers in interval notation)

Q: Find F as a function of x and evaluate it at x = 0, x = 7/4, and x = 7/2. 1-² sin € F(x) = F(0) =…

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Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: Let f(x) lim I→ 6+ if x = Calculate the following limits. Enter "DNE" if the limit does not exist.…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: We need to find maxima and minima.

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Q: 4) Activity 5: Check for Understanding (10 mins) NOV ob For the equation of y²dy = x(xdy - ydx)e*/y.…

A: We can find the degree of the given function and differential equations.

Q: 4. Solve the following equation by completing the square. Be sure to show all steps. (round answers…

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Q: 1. (x³ + xy²)y' = y³ Ssangen job10 2. (2x + y)dx= xdy 3. x³y' + x²y-y²= 2x4

A: Topic:- differential equation     Definition:- The order of a differential equation is defined to be…