Find two positive numbers that satisfy the given requirements. The sum of the first number cubed and the second number is 500 and the product is a maximum.

Q: Given that f(x) = x³h(x) h(1)=2 h'(-1)=5 Calculate f'(-1).

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Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2, x = 5 and x-axis.

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: A spherical balloon is inflated with gas at a rate of 800 cubic centimeters per minute. (a) Find the…

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Q: Given that lim_ f(x) = 1 lim_g(x) = -2 lim_h(x) = 0, X→2 x → 2 X→2 find each limit, if it exists.…

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Q: Find the centroid x of the plane region y=9-x^2 bounded by the positive x and y axes. O x = 3/4 O…

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Q: Let A(0, -2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA)=2. m(PB) (2) Convert the…

A: This question can be solved using the concept of distance formula.

Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: The height of a sand dune (in centimeters) is represented by f(t) = 850 - 2t² cm, where t is…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² - 6x + 4 lim X→ 2 X-2

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Q: Deriving the formula for volume generated by revolving the first- = quadrant area bounded by the…

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Q: PROBLEM NO. 8 GIVEN: f(x)=2x52x² +10x + 2 = 0 Using NEWTON'S METHOD, determine new estimate after…

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Q: Find the total number of permutations of the word 'ASSASSINATION', where all vowels are ALWAYS…

A: We have to find the number of ways

Q: e coordinates of a point on a circle with radius 20 corresponding to an angle of 3 your answers to…

A: Topic:- trigonometry ratio in circle

Q: Find the area of the region enclosed by the curve y=x²-3x³ + 2x² at interval from x=0 to x = 2. y…

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Q: given two vector find  A x B = C  and Convert  to cylindrical coordinates

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Q: (x²-x)dx

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Q: 6. f In² x dx

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Q: L₁ (r + 1)² dr

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: Q.9) A series E1 ((-1)*+¹) a) Converge by alternating series test c) Converge by integral test b)…

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Q: What is the exponential growth rate change of an investment that has a b=1.92?

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Q: For the function R whose graph is shown, state the following. (If the limit is infinite, enter '' or…

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Q: lim (SC - S(T)) where f(x) = -x²+x+6 f(7+h)-f(7) h h→0

A: f(x)=-x2+x+6= limh→0 f(7+h)-f(7)h limh→0 -(7+h)2+(7+h)+6-[-72+7+6]h limh→0…

Q: What is the area bounded by the curves x = 1/y, 2x - y = 0, x = 6, and the x-axis?

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Q: Convert 100 dollars to "widgets" (1 dollar = 3.94 widgets) 39.4 O 3940 394

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Q: 5 CSC x dx

A: Using following formula

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: 2. Evaluate the double integrals by iteration. whre B is the region 0≤x≤ 1, ² ≤ y ≤I JA dA

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Let's solve given diffrential equation.

Q: 9. Brett and Julia are getting married and the menu options at the wedding are as follows: Main…

A: Above question is solved.

Q: 28 Suppose cos(x) = and csc(x) < 0. Give all answers as exact values (no decimals 35 a. The terminal…

A: Use Trigonometric identities

Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: 14. √2-√x dx

A: SOLUTION-

Q: B C a A b Note: Triangle may not be drawn to scale. Suppose c = 11 and A = 55 degrees.

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Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x) = |x-1| In its domain. a.…

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Q: (Use symbolic notation and fractions where needed.) side of base: 6 height: 6 minimal surface area:…

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Q: #+2 Q.23) cos²3x dx = 24 a)- #+24 KT -24

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

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Q: H.W: Given the following table find x3, fo Af₁,Af₂, A² fo j xj Afo A² fo 0 fo 30 A² fo 4 20 Af₁ 2 14…

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: tion f(x) given below, evaluate lim f(x) and lim f(x). X48 X118 f(x) = x + √√x² + 3 answer below:

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Q: K|N sin cos 60 de

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 4. Let v = (v1, v2, v3), w = (wi, w2, w3) be two non-zero vectors not on the same line in R Suppose…

A: answer is in next step. please give a like !!!

Q: An analysis of the daily output of a factory assembly line shows that about 50t+t²- 1 tunits are…

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Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2x = 5 and x-axis.

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Q: Evaluate the integral. 2 x² + x + 1 6²7= Jo (x + 1)²(x + 2) dx

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Q: 17R(1,1,3), S(3,-3,6) and U(-2,4,7) are three vertices of parallelogram RSTU. a) Find the…

A: Given that the three vertices of a parallelogram RSTU are R1,1,3, S3,-3,6 and U-2,4,7 Now, let the…

Q: Prove the limit below exists and find its value to 6 digits but replacing n for a large value and…

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Q: (c) f(x) = x4 - 1 and g(x) = x4 – x³ – 3x² + 5x – 2 in F(R) -

A: HEre we have to find the GCD of the given polynomIal.