What is the value of a so that In (e") dx = 6? a A.) 0 B.) 1 C.) 2 D.) 3

Q: Let s = f(t) give an object's height, in feet, a seconds after it is thrown. After 3 seconds, tE fee...

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Q: dy +7"y – 7= 0 can be classified as dx The differential equation order 1, linear, and homogeneous or...

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Q: BThe distance from the point (-1, -2, 3) to the plane 2z = - 4x + 5 is [b] (input exact value in sim...

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Q: The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is g...

A: Note that:-Velocity of a particle is given by differentiating distance d(t) with respect to (w.r.t) ...

Q: -6 -5 4 The graph above is a transformation of the function a Write an equation for the function gra...

A: Vertex form of the parabola :            y =ax-h2+k ; where (h,k) is the vertex and 'a' is any const...

Q: y = 3x² – 1 from x = 0 to x = 1 . 3. Find the exact arc length of the curve

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Q: A child is on a swing. At its highest point, the swing is 5 feet above the ground. At lowest point, ...

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Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: a. lim f(x) = x→∞ Preview b. lim f(x) = Preview с. x→-7 lim_f(x) =

A: The given function is: f(x)=-(5x+3)2(x-1)(x+7)2(5x+3)

Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x...

A: We can use integration to calculate the area

Q: Suppose f is a quadratic function that has roots x = – 3 and x = 6, and f(0) = 15. We will w a funct...

A: Given: Root x=-3  and x=6 f(0)=15

Q: Regarding y as the independent variable and æ as the dependent variable, find the- y* + 5x²y² + 4yxª...

A: Given: - The curve is,y4+5x2y2+4yx4-2y=83 at the point (2,1) To find: - The slope of the tangent lin...

Q: 8- 6- 4- 2. The graph of f(x) is shown in red. Draw the graph of g(x) = - f(x). -8 -7 -6 -4 -3 -2 Ma...

A: The graph of the equation f(x) is given , find the graph of  1) g(x)= -f(x)  2) g(x)= f(x)-3 .

Q: d (x- 7)4 81. dx 3 2x

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Q: 5. If f cb 5dx + 4 V8x? . = 2, what is the value of b? a.) 2 b.) 4 c.) 8 d.) 9

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Q: In what quadrant is the point that is 51 away from P(1, 0) on the unit circle? II IV II

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Q: 14 If dx and y when x = 1, find y(2). 3x- 40 A 27 27 26 27 27 B)

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Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How fas...

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Q: In Problems 63–68, find f' (x) and find the value(s) of x where the tangent lině is horizontal. 65. ...

A: The given function,  f(x)=x2x+52

Q: W 34° T2°

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Q: 5) 3tan-1x + sin-x = 4

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Q: (sin x – 1) dx + (cos x + 1) dx = C.)-1 D.) - (1+) А.) —89 В.) —91 |

A: Using formula  ∫ Sin x dx = - Cos x + C ∫ Cos x dx = Sin x + C ∫ xn dx = [xn+1/(n+1)]+C   ∫(Sin x - ...

Q: Equation Find Given dy dx 3. y = (a) when x = 4 %3D dt dt dx dy (b) when x = 25 = 2 dt %3D dt

A: Solution: y=x 

Q: the rate of change in thr profit (p) with respect to the number of units sold (x) is 0.0006x^2 +10. ...

A: We can use the given equation to solve for profit

Q: C(x) = 2000 + 2x - 0.0001x (0 sxs 6000) (a) What Is the actual cost incurred in producing the 1011st...

A: Given query is to find marginal cost for the function.

Q: Evaluate the expressions. a) 14° b) - 14° a) 140-

A: a) 140=1

Q: Question 4 of 10 2 -10-8 -6 -4 -2 2. 4. 6. 10 -6 -10 y 10 4 -10 -8 -6 -4 -2 2 4 6 8 10 -6 -8 10 y 1...

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Q: . Find the period and phase shift of each of 1 a) y = - cot(6x – 4) 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: (a) Calculate the work required to pump all of the liquid to the top of the tank. (Your answer will ...

A: (a) Solution:-   Work required to pump water to height(h) =mgh  (where m= Mass of liquid , g= accele...

Q: Solve the differential equation (FODE)

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Q: You have been asked to build a ramp for Dan's Daredevil Motorcycle Jump. Base of the ramp is to have...

A: Base of the ramp is to have width x=100 feet and angle of inclination θ=10 degrees.

Q: Evaluate each expression. (a) (20b)° (b) 206° (a) (20b)0 = (Simplify your answer. Type an integer or...

A: Given:- (20b)0  20b0 To find:- Evaluate above given expression

Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocity i...

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Q: 9. An object is shot upwards from ground level with an initial velocity of 3 meters per second; it i...

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Q: A population of bacteria has 1175 bacteria in its starting population. The half-ife of this particul...

A: Given:   Bacteria : 1175     Days : 14

Q: Find equations of all lines having slope - 1 that are tangent to the curve y = x-5 Select the correc...

A: Given query is to find the equation of the tangy.

Q: The shaded band in the diagram is cut from a sphere of radius R. Show that the surface area of the b...

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Q: | (3t + t*) sin(2t) dt 3.

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Q: If f(x)dx = 5, f(x)dx =2, and f f(x) dx =-1, find f(x)dx. А.) —2 В.) 2 С.) —3 D.) 3

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Q: Evaluate f (5+ln æ)? -dx. Give your answer as a simplified fraction if necessary. The value of the d...

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Q: L:(sin x – 1) dx + ,cos x + 1) dx =? c)-1 а.) -89 b.) -91 d.) - (1 +)

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Q: 4. (x +y- 4) dx - ( 3x-y-4) dy = o when x=4, y=!

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Q: Suppose the function cos(t) is shifted 5 units upward. What is the equation of the new function?

A: To determine The equation of the new function if the function cos(t) is shifted 5 units upward. Conc...

Q: Consider the following rational function: 1 anx" + an – 1x" + ajx + a0 ... f(x) bmxm + bm – 1xm + .....

A: Recall: Horizontal asymptotes of a rational function : Consider the rational function               ...

Q: Differentiate the following functions using the limit method: 1) y = 7x - 3x" +x– 10 2) y = ;r - 8x ...

A: We will use limit definition to find derivatives of given function. Since , we know that f'(x)=limh→...

Q: Š F(x)dx = 5, f(x)dx = 2, and f(x) dx = -1, find ſ f(x)dx. If %3D а. — 2 b. 2 с. -3 d. 3

A: Topic:- integration

Q: Draw a graph of the cosine function with an amplitude of 12 (show at least 2 full periods).

A: Draw the graph of the cosine function with an amplitude of 12 . 

Q: 19. Find the total area between the parabola y = x² - 4x, the x-axis, and the ordinates x = -2 and x...

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Q: Linear differential equetion with constand coefficients -メ ダーンツ e

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Q: LINEAR DIFFERENTIAL EOQUATION WITH CONSTANT COEFFICIENT (STEP BY STEP SOLUTION) d2x dx 3x = -9t² – 1...

A: The given differential equation is; 2d2x/dt2 - 5dx/dt -3x =-9t2-1. t=0,x=1,dx/dt=0.