Find the coordinates of the center, foci, vertices, and the equations of the asymptotes of the conic section 25x² - 16y² + 250x +32y + 109 = 0. Graph the results to show the conic section.

Q: -2 t Evaluate √5+² dx

A: To solve the given definite integral problem.

Q: a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the…

A: As per the guidelines we are supposed to answer only first question and rest can be reposted..

Q: 2. A circular cylindrical hole is bored through a solid sphere, the axis of the hole is being a…

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Q: random variables X and Y have the joint density f(x, y) = {1.5 (x² + y²),0 ≤ x,y ≤ 1, 0, elsewhere.…

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Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: At what point do the curves r₁ = and r₂ = intersect? ( ) Find their angle of intersection, 0…

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Q: Use the divergence theorem to evaluate ]] F .dɔ̃ where F = xyi – ¹⁄y²j+zk and the surface consists…

A: Here, the surface consists of the three surface z=4-3x2-3y2; 1≤z≤4 on the top x2+y2=1, 0≤z≤1 and z=0…

Q: Find the general solution of the differential equation. y (4) + 2y" + y = 9+ cos(4t). NOTE: Use C₁,…

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Q: For f(x, y)= e sin(25x), evaluate fy at the point (77, 0). Of,(7,0)=50 O fy(7,0)=0 Of(7,0)=51…

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Q: Find 10 partial sums of the series. (Round your answers to five decimal places.) 00 n=1 15 (-2)^

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Q: 2. A function is said to be if, graphically speaking, you can trace the entire curve without any…

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Q: 1. Determine the area of the region under the curve y=x√(x² - 1) 2. Determine the area of the region…

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Q: Rewrite the following equation with the variables separated. tan(y)y' = 4 cos(x) O sin(y) dy = 4 dx…

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Q: Determine the location and value of the absolute extreme values of f on the given​ interval, if they…

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Q: An annular cylinder has an inside radius of r and an outside radius of r2 (see figure). Its moment…

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Q: :) [x²ai 6.) sinxdx

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Q: f" s [0, π]. Also, find the smallest value of x at which the average value occurs. Given that sin…

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Q: dx Evaluate So x²+4

A: Follow the procedure given below.

Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² + y²

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Q: An aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

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Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Q: Let D be the planar region bounded by y = 0, y = x², and x = 1. The integral ff cos(z² + y²) dA…

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Q: Solve the differential equation by variation of parameters. 1 7 + ex y(x) = = y" + 3y + 2y =

A: The given differential equation is;  y''+3y'+2y=1/(7+ex).

Q: Sketch the region enclosed by the curves and find its area. 1 √1-9x2¹ Y=2 NOTE: Enter the exact…

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Q: Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the…

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Q: Solve, finding all solutions in [0,2x) or [0°,360°). 2 sin‘x+ sinx=0 2

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Q: Determine where the function m(x) = x + 1 (x-1)(x-7) is continuous. The function is continuous on…

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Q: Find aw/as and ow/ot using the appropriate Chain Rule. Function Values w = y³ - 7x²y x = e³, y = et…

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Q: If u(t)=sin(t), cos(4t), t > and v(t) = , use the formula below to find the given derivative. [u(t)…

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Q: The mess in a house can be measured by M(t). Assume that at M(0) : = 0, the house starts out clean.…

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Q: Differentiate implicitly to find the first partial derivatives of z. 7x² + 3y² + 11z² = 36 əz əx əz…

A: Differentiate implicitly to find the first partial derivatives of z.   7x ^ 2 + 3y ^ 2 + 11z ^ 2 =…

Q: List the first five terms of the sequence. a1 = 3, an+1 = 5an - 5 a1 a2 a3 = a4 = a5 =

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Q: Use integration by parts to solve for J x secx tanx dx.

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Q: e) x - 4y= 26er r

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Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: Evaluate the definite integral. 3 1₁(x-41 4|x) dx

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Q: Consider the following. w = xy cos z, x = t₁ y=t5, z = arccos t (a) Find dw/dt by using the…

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Q: 6. (8x³ − 6x² + 12x − 9)dx (x²-1)³ √x 8. [ V4 – x2 xdx 10 9. § (2x³ + 5)¹⁰ x² dx 7. S - dx

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Q: = Find the area of the region bounded by the curves y on the interval [0, 1] as seen in the shaded…

A: This question can be solved using the concept of area bounded by curves.

Q: Use the graph to find the point(s) of inflection of f. (Give your answer in the form of a…

A: Given: the graph is given we want to find inflection point and concave down range         Inflection…

Q: (a) [2 2 2x dx

A: Note: As all are different questions, as per our company guidelines we are supposed the answer the…

Q: Evaluate the integral -1/4 7x/4 S (sin x + cos x) dx using the fundamental theorem of calculus.…

A: We have to find the area is -π/4 or not.

Q: p = 3 csc()csc (0)

A: find an equation in rectangular coordinates for the EQUATION GIVEN IN SPHERICAL COORDINATES  p=…

Q: 23. Given f(x) is graphed below, sketch f-1(x) on the coordinate plane with f(x). (1,2) -5- 0 (1, 1)…

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Q: + 2x)² 4x +2

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Q: At how many points do the curves r₁(t) = ((t + 1)², — t² − 2t, t+2) and r₂(t) = (1 – t², t, t) -…

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Q: For f(x) = (x + 1)²-3 where x > -1, find: a. The inverse function, f-¹(x) b. The domain of f-¹(x) c.…

A: Given f(x)=(x+1)2-3 We know that, A function g is the inverse of function f if for y=fx,…