An open-top storage box with a square base has a capacity of 32 m². Find the dimensions that will minimize the surface area of box.

Q: Find the general solution of the differential equation. y(5) — 11y(4) + 29y"″ − 11y" + 28y' = 0.…

A: Let's solve given diffrential equation.

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A: Solved below.

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Q: If sin(0) and is in quadrant I, find the following: 7 Give exact values. No decimals allowed! cos(0)…

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Q: Consider the following equation. 6² - x = 36 Find any Intercepts. x-Intercept (x, y) = (…

A: Given equation of curve:- 6y2-x=36  Find:- X intercepts, y intercepts, symmetry and graph of curve

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A: This question can be solved using the concept of graph of functions. We need to find solution set…

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Q: (c) I² +4 3x³+4x² - 4x [3 -dx

A: Here we have to find the integral.

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Q: Graph the function by using transformations of the graph of y= points on each side. p(x) = 1 (x-2)²…

A: The graph of the function y=1x2 is:

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Q: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: What is the equation of the tangent line at 3x+1 0₁ = 1² of f(x) = ² 0, 2 X-2

A: The equation of tangent is :

Q: Find the Consumer's Surplus corresponding to q=900 units. (Do no rounding of results until the very…

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Q: Solve 2 sin² (x) - 3 sin(x) + 1 = 0 for all solutions 0 < x < 2π x= Give your answers as a list…

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Q: Sin (Imx) = h+, hx +,hax

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Q: Evaluate the following integration.

A: Let Sinx=t

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Q: Suppose f(x) is the total number of children that have a disease, and is the number of days since…

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Q: 5 Find a parametrization for the line segment joining the points (0, 2) and (4,0) using the angle in…

A: A parametrization for the line segment joining the points (0,2) and (4,0) using the angle θ in the…

Q: - Simplify: sin(x)tan(x)=1- 1-cos²(x) cos (x)

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Q: A company wants to start a new clothing line. The cost to se up production is 35, 000 dollars and…

A: The solution is given below

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A: We first need to find complementary solution Auxiliary equation is given by m3-2m2-m+2=0…

Q: 1 2. S- 9y²+64 dy

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Q: Solve the application problem involving a rational equation: Kellen's boat travels 12 mph. Find the…

A: This is a problem related to distance and time calculation. Based on the general formula and concept…

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Q: Explain why S is not a basis for P₂. S = {1, 6x, -2 + x²,4x} O S is linearly dependent. OS does not…

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Q: The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a…

A: Given: The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams)…

Q: Determine whether the series below converges or diverges. If the series converges, find its sum.…

A: Expand the given summation

Q: ind the volume generated by revolving the area 1 unded by y = 2 x³ + 15x² + 56x Round the answer to…

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Q: 1.3 domain: What is the domain of y = ln (x² - x - 6)? help (inequalities)

A: The function is  y=ln(x2-x-6)

Q: 8 16. Given that sin x = [ k=0 (-1) k (2k + 1)!" 2k+1 x² for all x, find the Taylor series for f(x)…

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Q: Let y = √r and y = 2³, draw the region bounded by the curves. Then, use the washer method to find…

A: In this question we have to find the volume of the region bounded by curves using washer method.

Q: It has been determined that the cost of producing x units of a certain item is 10x + 365. The demand…

A: topic - functions

Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, ....)…

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Q: If tan(0) Hint = sin(0) = cos(0) = sec (0) = 15 - 8 ) 0 ≤0 ≤ 90°, then the exact value of

A: Here we have to find the other trignometric function.

Q: Find the exact length of the polar curve. r = 0², 0≤ 0 ≤ 4π X

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Q: A chemist has three different acid solutions. The first acid solution contains 20% acid, the second…

A: This question can be solved using the concept of system of linear equations.

Q: t².edt J (P)

A: Solve the following

Q: It tan(x) sec²(x)dx (a) Evaluate the integration by setting du = sec²(x)dx; (b) Evaluate the…

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Q: 8. (x2 – 1)y" + 2y – (x – 1)(x + 1)2 = 0

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Q: 6. Find y" give y = 7³x a) 21³x In(7) b) 63³x In(3) c) 3(7³x)ln(3) d) 9(7³x)(ln7)

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. -2t y"…

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Q: +∞ Σ n=1 1+ sin² n 10η

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Q: a B Find: b = Note: Triangle may not be drawn to scale. Suppose a = 10 and A = 60 ° C= C B = b A

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Q: A kids Ferris wheel has 8 equally spaced cars. What is the angle of elevation of the child looking…

A: Given : angle of elevation is the upwards angle from the horizontal line to  a line of sight from…