40- 30 20 10- -10 10 10 20 30 40 50 60 Christian is a lifeguard and spots a drowning child 60 meters along the shore and 50 meters from the shore to the child. Christian runs along the shore for a while and then jumps into the water and swims from there directly to the child. Christian can run at a rate of 4 meters per second and swim at a rate of 0.9 meters per second. How far along the shore should Christian run before jumping into the water in order to save the

Q: Consider the integral fa³ In(a) dæ: Applying the integration by parts technique, let In(x) Ա dv = x3…

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Q: The linear density of a rod 3m long at a point x meters from one end is ke-3x kilograms per meter.…

A: Solution is given below:

Q: Consider the function f(t) = 3 sec²(t) - 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: Find the area bounded by y = x and y = x³. 02 00 01 O 2 01 4

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Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

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Q: Solve the equation (x+3x³ siny) dx + (x4 cosy) dy = 0

A: Here we have given a differential equation :(x+3x2siny)dx+(x4cosy)dy=0      ......eq(1)

Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals…

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Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: The Maclaurin series of g(x)=sin (x) is ?

A: Maclaurin series is given by:

Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: If what does the following integral equal? 1 d(v)dv= 8 - d(v)dv = 20 and 8 [*d(v)dv = 6.8 7

A: To evaluate the given definite integral.

Q: O

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Q: Given the function graphed below, evaluate the definite integrals. -1 4 3 2 1 1 -1 -2 -3 -4+ […

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Q: 12 Sf x² ydxdy 01 In2 2 11₂ SS 2xe dxdy 0-1 3 1 2xy SS- -dxdy 10x+1 4√x 2 S S x²y dydx 00 11-y S S…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: -10 70 60 50 40- 30- 20 10 10 10 20 30 Dmitry is a lifeguard and spots a drowning child 30 meters…

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Q: What part of this graph is the solution area for a system of inequalities? The blue and red parts…

A: Let's find area of inequalities from given graph.

Q: (y - k)² a² (x - h)² b2 1

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Q: Let y(x)=−3/x^2. Find y′(−3). Enter the exact value, i.e., no decimals

A: given  y(x)=-3x2=-3x-2

Q: What are the parametric equations of x - 2y + 3z - 1 = 0?

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Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: 5. Use the divergence theorem to evaluate the surface integral ff, F. ds, where S is the sphere x² +…

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Q: A particle is moving with a position function given by s(t) = 6t² - in metres and time in seconds.…

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Q: nd f(7zº + 5x³) dx Find + C

A: Given:     ∫7x6+5x3dx=∫7x6dx+∫5x3dx=7∫x6dx+5∫x3dxwe know that ∫xndx=xn+1n+1

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = [tªdt.…

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Q: Which equation represents a line that goes through the points (0, 1) and (1, 0)? y = -(x + 1) y = 1…

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Q: The marginal revenue from the sale of x cans of air freshener is given by 4.4 -0.32√x dollars per…

A: In here, the marginal revenue is given as a function of x. So, we will use the formula: Marginal…

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A: Given tree diagram shows all the possible combination of "cooldrinks", "chocolates" and "chips or…

Q: A writer wrote 850 words on the first day, 730 words on the second day and 610 words on the third…

A: Given: A writer wrote 850 words on first day, i.e. d1=850 Similarly for second and third day…

Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: Suppose that h(x) = f(x) g(x) and that we know the following f'(3) = -1, g(3) = 2, & g'(3) = -5.…

A: Topic:- calculus

Q: A smooth curve C is defined by some vector function R(t) with R (7) 2 = = (π,0,−2) and R' (t) = (2,…

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Q: 3. Give an example of a situation in which composite differentiation might be used. Give examples of…

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Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Here we will use the chain rule i.e., if u and v are function of t with f=uv then…

Q: X √x dx 5-х

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Q: Let f(x, y) = x6y4. Round the components of your answers to three decimal places. (a) At the point…

A: Please see the below picture for detailed solution.

Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

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Q: Consider the function f(x) = 10x¹0 + 3x7 - 8x4 - 2. An antiderivative of f(x) is F(x) = Ax" + Bx" +…

A: Given, f(x)=10x10+3x7-8x4-2

Q: If f(x, y) = x²y and ʊ = 47 – 37, find the directional dervative at the point P = (3, 6) in the…

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

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Q: 2 x²√x²+9 dx

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Q: A particle is moving with a position function given by s(t) = 6t² - ³ with position in metres and…

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Q: Question 17 > At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 16…

A: Please see the below picture for detailed solution. I answered question number 17.

Q: Find the equation of the tangent line at the point 0, In 3 3 for f(x)=In 3 e²x² 2e +e²x

A: Topic:- application of derivatives

Q: Factor x^2 + 10x + 12. (x + 5) (x + 7) (x + 10) (x - 12) None of the answers are correct; this…

A: Given: Factor x2+10x+12

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given,           Rx=7x and Cx=160-2x+x2To find : How many pizzas sold maximizes the profit.

Q: -5 0x2 0<x<2 2 Over what interval is f(x) concave down? Ox<0 y=f" (x) 5

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Q: Explain the steps you would take to find the derivative of f(x) = (-)e -3x+tan(3x-5)

A: Given: f(x)=12e-3x2+tan(3x-5)