lecture(12.4): Here are the final grades for the students who took STAT683 last semester. 84, 72 80 , 77, 78, 81, 64, 86 (a) what is the mean of these grades? (b) what is the standard deviaton of these grades? (b)

Q: 2) Given: x = t³ + 1, y = t² – t a) Find dy/dx and d²y/dx². b) For which values of t is the curve…

A: The given functions are: x=t3+1, y=t2-t

Q: Calculate the definite integral. 10 8. dx X. 2.

A: We can solve this as follows:

Q: Evaluate the expression under the given conditions. 3 sin(0/2); tan(0): O in Quadrant IV (assume 0 <…

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Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

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Q: Solve the following quadratic equation. Write your solution as a set. 6x2 + x − 2 = 0

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Q: Determine the area that lies inside r = 3 + 2 sin 0 and outside r = 2 (the green region below). r =…

A: In this question, we need to find the area of the region that lies inside r = 3+2 sin θ and outside…

Q: So, the volume of the solid of revolution is Volume = V = TI (9 - x2)2 dx. To find the volume,…

A:

Q: the integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: Given that the integrand of the definite integral is a difference of two functions. Here we have to…

Q: Example 4 Identify and sketch the curve 153x-192xy +97y2 - 30x- 40y – 200 = 0 !!

A: Given:     153x2-192xy+97y2-30x-40y-200=0  We have A=153, B=-192, C=97 So, cot2θ=A-CB=153-97-192…

Q: A particle moves along the x-axis such that at any time t > 0 its position is x(t), its velocity is…

A:

Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q - 0.7q+620. The…

A: Find your answer below

Q: Q1. Find by implicit differentiation; a) an equation of the normal to the astroid x/3 + y/3 – 4 at…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: #3: Find the maximum of the following function: h(x, y) = In(x40 y8) given the constraints: 5x² + y²…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information sec(x) = 4, x in Quadrant IV %3D…

A: Given: secx=4, x in Quadrant IV   We know that; The trigonometric identities; 1). sin2x+cos2x=1 2).…

Q: A rectangular prism has a height of 11.5 inches, a length of 9.6 inches, and a width of 2.10 inches.…

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

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Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

Q: dx sinx + cosx * 20. Evaluate tan{ 1 + tan; ) +C |+C ) m1- un| +C D) tan(1- tan )+C tan B) In1+tan

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Q: A = 13 ;Prove A2 - 5A = 21

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Q: Solve D.E using bernouliis equation dy – 2x · = x(x+1)y' dx

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Q: Solve the differential equation dR = a(R? + 9). dx Assume a is a non-zero constant, and use C for…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: 64. 8

A: We have to test the convergence of given series

Q: The gcd of 7544 and 115 is: O 23 O 15 O 3

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Q: hit

A: Given,  h(d)=-1/125d^2+d where, Horizontal distance is d. Height is h.

Q: Consider the following function. H(x, y) = 10 ln(x2 + 3y3) a) Find fxx(2, 3). b) Find fyy(2, 3).…

A: H(x,y) = 10 ln (x2+3y3)a)fx (x,y)=10x2+3y32x+0 =20xx2+3y3differentiate partially w.r.t x…

Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

Q: ~3 (x/x+1)dx

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: (kx – 1 ifx< 2 G(x) = kx? 2. if x 2 2

A: the given function,   G(x)=kx-1if x≤2kx2if x≥2

Q: Which integrals are improper? Explain your reasoning

A: this question can be solved by applying the two conditions for an integral to be improper.

Q: Solve th D.E using Exact -(3x² – 6.xy)dx +(-3xr' – 2y)dy = 0

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Q: 4. If ) Cn (x + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: ∑n=1∞cn(x+2)n Since series convergence for -5&lt;x≤1Then Interval of convergence is (-5,1]Let R be…

Q: sinx 18. Supposed Ax) = [ V1+t* dt and g(y) = | f(x)dx , what is the value of g' 15 A) 2 C) B) D)

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Q: Using integration by substitution in ſ x³(x6 – 2)³dx, what is du? A. xdx В. бх5dx С. (х6 — 2)dx D.…

A: ∫x5(x6-2)dxPut x6-2=udifferentiate…

Q: 4. [Geogebra Question] Let f(x) = (1– x) In(x*) +3.0225887223. Use Geogebra to find the definite…

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Q: 16z(2r² + 1)°dr

A:

Q: Find the volume of the solid generated byrevolving the specified region about the given line. R…

A: Let's find.

Q: -(-3у?-у-2)dy 2y3+y2+4y

A:

Q: S(sin2z – 3cos2z)°dz

A: Here, (sin 2z-3cos 2z)2 =sin22z-6sin 2zcos 2z+9cos22z=sin22z+cos22z-3(2sin 2zcos 2z)+8cos22z=1-3sin…

Q: 8. y = x³ + x , 0 < x < 2

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Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0).

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Q: Find the gradient of the function at the given point. g(x, y) = 3xellx, (10, 0) Vg(10, 0) =

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Q: The improper integral 1 xp- (x + 4)4 is convergent. Select one: True O False

A: To solve this question we need to apply the concept of convergence and divergence of improper…

Q: 2+ y =x+ - 2x3 1 y = 0 2 -1

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Q: 00 1 25. nº – 7 n=1 00 .3 IM:

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: b) Find the value of a such that the average of the function 100x is equal to 100 in the interval a…

A: The average value of the function 100x is equal to 100 in the interval a≤x≤1

Q: If m is a positive integer, does 6 divide (2m)(m+2)(3m+3)? True False

A: Here, the given number is: (2m)(m+2)(3m+3)=2(m(m+2))3(m+1)=6m(m+1)(m+2) because multiplication is…

Q: 13. ап V21+3п 15. ат — 2" cos пл

A: Follow next step