Obtain the limited area between the following curves 5x² + 6y² = 84; 4x² - y² = 12

Q: a preschool order $2050 in books and supplies.Suppose that the bookstore offered the school a loan…

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Q: Find the area of the region bounded by the graphs of ƒ(x) = x³ + 4x² − 12x and g(x) = −x² + 2x.…

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Q: 10. Find the max/min of f(x, y) = x²y on R = {(x, y): x² + y² ≤9}- I

A: f(x,y)=x2y on R={(x,y):x2+y2≤9}f(x,y)=x2yg(x,y)=x2+y2−9Using the power Ruleddxxn=nxn−1

Q: Find the area under the curve y = 2x-3 from 7 to a = t and evaluate it for t=10, t= 100. Then find…

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Q: For the curve given by r(t) = (9 sin(t), -2t, -9 cos(t)), Find the unit tangent T(t) = (000) Find…

A: For the curve given by , to find the unit tangent vector, unit normal vector, and the curvature.

Q: So Find the EXACT answer, then round it to THREE decimals. Evaluate the improper integral: 1 4+x² dx

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Q: If f(x) = lim f(x) = X-4 -7 for x = 4, {2} 2x+7 for x #4 then

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Q: 15. Sketch the region of integration of S evaluate it. Vy sin ydydr and reverse the order of…

A: I=∫01∫2x22xysin⁡ydydx

Q: Consider the two functions y₁=x²-3 and y2 = b on the interval [-a, a], if a = 11.3. What value does…

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Q: Consider two functions y₁ = f(x) and y₂ = g(x), and that y₁ + y2 except where they intersect. If…

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Q: Find the equation of the tangent line to the curve at the point corresponding to t π x = t sint y =…

A: x=tsin⁡ty=tcos⁡tProduct Ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

Q: Given: (x is number of items) Demand function: d(x) 2420 √I Supply function: s(x) = 5√√x Find the…

A: Demand function: d(x)=2420xSupply function: s(x)=5x

Q: Of all rectangles with a perimeter of 25, which one has the maximum area? (Give the dimensions.

A: We can find the dimensions as below.

Q: Solve the initial value problem y(t) = = dy dt Y t+1 + 4t² + 4t, y(1) = 8

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Q: Find the local maxima and minima for the function. Find the intervals on which it is increasing and…

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Q: A baseball team plays in he stadium that holds 68000 spectators. With the ticket price at $9 the…

A: We have given that stadium holds 68000 spectators.When the ticket price at $9 the average attendance…

Q: Given: (x is number of items) Demand function: d(x) = 400 -0.4x Supply function: s(x) = 0.4x

A: Demand function: d(x)=400−0.4xSupply function: s(x)=0.4x

Q: -3 If A = [¯ 1¹ ²], B = [~ 3³ 2], and C = =[2], find 4 21 A²+ BC.

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Q: Solve the separable differential equation for u dudt=e6u+5t. Use the following initial condition:…

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Q: 9 Consider the function f(x) = 6x⁹ + 6x7 - 7x² - 4. Enter an antiderivative of f (x). Do not enter…

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Q: 16- 14- 12 10- 8. 6. 4. 2 2 Estimate the instantaneous rate of change at x = = 3 Your estimate needs…

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Q: For every positive number a the functions sin x and cos x are orthogonal on the interval [−a, a].…

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Q: Find the length s of the arc that subtends a central angle of measure 4 rad in a circle of radius 5…

A: central angle of measure 4 rad in a circle of radius 5 cm.

Q: csc csc(x) dx Expand fraction by csc(x) + cot(x): csc(x) (csc(x) + cot(x)) csc(x) + cot(x) 1² dx

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Q: If-x-2+5 ≤ g(x) ≤ |x − 2|+5 for 1 ≤ x ≤ 3, evaluate lim, 29(x). Provide your answer below: lim g(x)…

A: Given,  then we have to evaluate

Q: 3x - 6 Given a function is defined by f(x) = x² + 3x- 10 for what value(s) of x does the function…

A: f(x)=3x−6x2+3x−10

Q: An open-top rectangular box is being constructed to hold a volume of 350 in³. The base of the box is…

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Q: A lim x+1+x-1 is A. 1 B. 2 C. 88 D. 00

A: limit

Q: Which step is part of finding the derivative of the function below? The correct choice may not be in…

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Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

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Q: Evaluate the integral. 2 [₁² (4x³² + (4x³ + 3x² + 1) dx =

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Q: Using the substitution u 52 — 2, = A B Julou z du 2. [IV αν u z du ÷ / (u² +2¹) ou du ½ / [(u ² + 2u…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated by…

A: Region is bounded by y=4−6x,y=0, and x=0Rotating the region about x-axisUsing the disk method

Q: Torm. y=4-2x +9x² y=4-2+18x y=4-2x+18x y=-2 + 18x y = -2x + 18x none of the above Find the…

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Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

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Q: Evaluate the integral 41 [ 2² (2³ – 4) ¹¹ d by making the substitution u = x = x³ - 4.

A: use appropriate method to solve the integral

Q: 10 Find the derivative of: 4√ Type your answer without fractional or negative exponents. Use sqrt(x)…

A: Explaination of the answer is as follows

Q: The constant solution y ≡ π/2 of the equation y' = cos(y) is stable , true or false ?

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Q: Calculate P(FIE), if P(E|F) = 0.02 P(E) = 0.86 P(F) = 0.26 Round your answer to five decimals.

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Q: Use the law of sines to find the indicated angle(theta). Assume c=30. A=120(degrees),…

A: Given some values of angles and the length of a triangle.

Q: For f(x)=√16-2x (a). find the domain. Write your answer in interval notation. (b). Graph f(x)=√16 -…

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Q: Dengue-fever viruses are carried by mosquitoes. There are several different serotypes of the dengue…

A: From the given statement

Q: A four-digit PIN code is required for a bank's ATM card. An encrypted code is stored with the bank…

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Q: Convert the equation r= 10 sin 0 to Cartesian coordinates. Describe the resulting curve. Choose the…

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Q: How is the graph of y = i and ii 1) horizontal compression by a factor of 1/2 II) translation 2…

A: 1). The transformation of  can be obtained by the expansion of the graph of  horizontally by a…

Q: The function f is given by f(x) = (2a³ + bx)g (a), where b is a constant and g is a differentiable…

A: First we differentiate f(x) w.r.t x

Q: Set up an integral to find the area of the region above y = x² - 4x and below y = 2x ○ ſ₁¹ (2x − (x²…

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Q: If y = 8 sin 2x cos 2x, then A 128 sin 2x cos 2x C. 64 sin 4x B. 128 sin 6x D. 8 sin 2x cos 4x

A: If , then to find .

Q: Approximate the definite integral using the right hand sum with n=3 (three subdivisions) 5 -1 x² dx

A: To approximate the following definite integral by using the right hand sum with  (three…

Q: For each value below, enter the number correct to four decimal places. Suppose an arrow is shot…

A: Suppose an arrow is shot upward on the moon with a velocity of 39 m/s, then its height in meters…