A curve has an equation  y=2x2+5x+c where c is a non-zero constant. Given that the roots differ by 3, determine the value of c. Give your answer as a fraction.

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: Let S be the part of the sphere x^2 + y^2 + z^2 = 1 that lies above the conez = sqrt(x^2 + y^2).…

A: The objective of this question is to evaluate the surface integral of the function sqrt(x^2 + y^2)…

Q: Find the nth term of the geometric sequence whose = 2 and common ratio is 3. initial term is a 1 ап…

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Q: Solve sin(x) = 0.64 on 0 < x < 2π There are two solutions, A and B, with A < B A = 0.6945 B = Enter…

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Q: Find an equation of the tangent line at x = a. 2 y=x-xia=2

A: y=x−x2;a=2Using the power ruleddxxn=nxn−1

Q: Suppose according to a large research poll in a certain year, 59% of respondents agreed that the…

A: a. To find the probability that a respondent agreed with both statements, we can use the formula for…

Q: Evaluate the integral using integration by parts √(x² + 2r) e³² dr

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Q: 2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ t≤ 5, the velocity…

A: The answer is given as follows:(a): ∣v(t)∣=∣−2+(t2+3t)56​−t3∣=2 solve t from this equation.(b):…

Q: (a) Find the length of the curve y = x4 - 16 + 1 1 ≤ x ≤2 2x2

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

Q: Find the volume of the solid that results when the region enclosed by y = √√x, y = 0, and x = 9 is…

A: Given that the region is bounded by the curves

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: The surface are is  2π∫03​3x31+x4​​dx=258.85Explanation:Steps and explanations are as follows:In…

Q: Find the first partial derivatives of the function u(r,t) = 3 sin(r cost)). 1. ur(r,t) = = 2.…

A: Explanation is given below:Explanation:

Q: please solve this

A: Ans :  Volume = 2.24 cubic units ( approximating upto 2 decimal places)Explanation:Explaination:

Q: Help this question

A: Therefore, the directional derivative Da​f(a) is 16.Explanation:To find the directional derivative…

Q: A company uses the model R(x) = 35x^2 - 5/3x^3, 0&lt;=x&lt;=10   to relate its revenue, R, in…

A: Therefore, the point of diminishing returns for this model is at 7 million dollars.Explanation:To…

Q: t 5 12 Suppose ƒ (x, y) = 2x² - 1xy + 1y², P = (−3, 2), and u = = (1/3, 1/3 ) . A. Compute the…

A: The answers are as follows:A.∇f=(4x−y)i+(2y−x)j. B.∇f=−14i+7j. C.(Du​f)(P)=1.08.Explanation:Steps…

Q: Determine which sets are vector spacesunder the given operations. For those that are not, list all…

A: The objective of the question is to determine whether the set of all real numbers, with the standard…

Q: Question 6 Using the definition of the slope of a tangent line to a curve, find the slope of the…

A: a)f(x) =

Q: Find the indicated partial derivative. f(x, t) = x5e-ct fttt 0 ftxx = 0 × ×

A: Answers:  fttt​=−c3x5e−ctftxx​=−20cx3e−ctExplanation:Step 1:

Q: PLEASE ANSWER THE QUESTION ACCORDING TO INTERVAL NOTATION. AND PLEASE WRITE THE ANSWERS AT THE END…

A: a) (−23pi​,−2pi​)b) (0,0)c) (0.57,0.07904)d) (−6.18,−pi)∪(0,0.57).Explanation:a. Given the function…

Q: No hand written responses.

A: (A) N is discontinuous at t2, t4, t5, t7 and t8 . (B)Option A. limt→t6​​N(t)=4 Option A. N(t6) = 4…

Q: Find the volume of the solid generated when the region enclosed by √√√x, y = 6 — x, and y: 0 is…

A: y =√xy=6-xy=0 revolved about the x-axis

Q: What is the maximum rate of change of f(x, y) (2,0) 2x+2y 4x²+4y2 2 0 None of the above x²+y at the…

A: at the point

Q: 1. Evaluate fxsec²xdx

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Q: 20. Given a = [3, −5, 1], b = [−2, 4, −1] and d = [7,3,-2], find a) b.z b) ax c c) 0, the angle…

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Q: Determine a value for k such that the two planes are coincident. -3y+z=-27 -x- 3x+k²y+kz = k* a. k=3…

A: Final answers: (1)   d (2)  cExplanation:###(1)For two planes to be coincident, their normal vectors…

Q: Continuous Compound Interest Jesaki Bank offers a 10-year CD that earns 2.5% compounded…

A: 1) The investment will be worth approximately $15,963 at maturity.2) It will take approximately 4.1…

Q: Set 2π 1 +3 up and evaluate the definite integral for the area of the surface generated by revolving…

A: The required answer is 258.85 square units .Please find the attached file for details...Thank…

Q: Evaluate the integral. (Use C for the constant of integration.) Sin(x+ In(x + √x-6) dx x2

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Q: 20. Given a = [3, −5, 1], b = [−2, 4, −1] and ♂ = [7,3, −2], find a) b.z b) ax c c) 0, the angle…

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Q: Consider the following time series data Month 1 2 3 4 5 6 7 8…

A: The answers are given below please have a look.Explanation:

Q: 2. Here, ƒ is the function given by f(x) = Find the limit, if it exists lim x→2 = arcsin (#) f(x) −…

A: The given function is To find

Q: Evaluate the integral √¹²x² tan¹(x)dx Give your answer correct to 2 decimal places in degrees.…

A: Therefore, the value of the integral is approximately 13.75  degreesExplanation:To solve the given…

Q: 8. Given y = log1/2x: a) Solve for the x-intercepts. b) Explain why the solution to log 1/24 must be…

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Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: Answer : option (b) 2eExplanation: (7) Given,  f(x)=exx​ We know that,…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The equation of the plane is3x+7y−8z=40.Explanation:Steps and explanations are as follows:In case of…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: 9)The correct answer is: "False". A normal vector to a line is perpendicular to that line, not…

Q: Two helicopters leave a heliport at the same time. The first flies 190⁢km/h in a direction of 290…

A: The distance between the two helicopters after three hours is 369 kilometersExplanation:Step 1:…

Q: ☐ Let 60, 61. Which of the following must be true if y = log(x)? Check all that apply. ☐ y = b² 1 y…

A: Option C is correct Option D is correct Explanation:

Q: Can you please provide me with a detailed problem and solution that helps me to understand the…

A: The objective of this question is to understand the concept of surfaces and level curves in…

Q: No hand written responses. I need help with a step-by-step breakdown in laymen terms for each part…

A: Answer AOption A , t2​, t4​, t5​, t7​, t8​Answer Blimt→t6​​N(t)=7N(t6​)=7Answer CThe Limit does not…

Q: Z Y X X y Z Suppose y=3 cm, Y=1.5 radians, and X=1.2 radians. Determine the following quantities.…

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Q: (Text' . | Find a ⋅ b if |a| = 5, |b| = 4, and the angle between a and b is radians. 8 • a b =

A: The formula for the dot product is : a⋅b = ∣a∣ ∣b∣ cos(θ)a⋅b  = 5* 4 *cos(π/8)a⋅b   = 18.4776…

Q: Find the EXACT value of the area of the surface obtained by rotating y = x³, for 0≤ x ≤ 2 about the…

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Q: The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.04t³ +…

A: (A) S′(t)=0.12t2+1.6t+8 (B) S(4)=53.36  and  S′(4)=16.32 (C) S(12) gives the total sales of the…

Q: 4. Find the inverse of the function, s(t) = √3 - t² - 6

A: To find the inverse of a function y=f(x) , use the following steps .Let y= f(x)Swap the variables x…

Q: Evaluate the integral using partial fraction method (3x² + 2) dx (x+2) (x²+4)

A: The given integral

Q: Find the first partial derivatives of 4x - f(x, y) = = 3y 4x+3y at the point (x, y) = (2,4).

A: f(x,y)=4x−3y4x+3y at the point (x,y)=(2,4)Using the quotient…

Q: Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact…

A: The area is:A=12253​Explanation:The given curves are: f(x)=x3,g(x)=x2+6x To visualize the bounded…

Q: +a2+C √ √√a² + u²du = ½ (u√u² + a² + a²]n]u + √u² + a² 1) + T 114

A: