Find three positive numbers whose sum i 21 and the sum of whose squares is as small as possible. Be sure to explain why your answer leads to the smallest sum.

Q: Find an equation for the hyperbola described. Graph the equation. Foci at (3,7) and (9,7); vertex at…

A: Plot the foci and vertex and try to observe the position of other vertex and then go ahead.

Q: f(0) = 2 cos 0 + (sin 0)².

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Q: 1. Evaluate the double integral [ry? dA, where D is the region enclosed by the y-axis and the…

A: The figure of the region shown below÷

Q: Express the equation in logarithmic form. 1 wlr -4 = 81

A: Given query is to convert into logarithmic expression.

Q: Find the rate of growth after 6 hours.

A: To find the rate of growth after 6 hours.

Q: Find the volume of the given solid region in the first octant bounded by the plane 15x + 15y +9z =…

A: See this solution in below.

Q: 4. Martin's family drives 300 km from their home to a family reunion. His cousin Sherry and her…

A: Since both reach the party at the same time so both take same amo

Q: Solve for the general solution of the given DE: O Inlx| + xy = C O Inlyl + xy = C O Inlyl + x^-1…

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Q: Finding the intercepts, asymptotes, domain, and range from the... OF BOASADRO Shom all asymptotes…

A: Given query is to find characteristics of the function.

Q: f(x) = 2x + 3 if x <3 if x ≥ 3 - 3 Find lim f(x), or explain why it does not exist. X-3

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Q: State the exact value of all six trigonometric function values of 3, given that a = 33 m and b = 56…

A: a= 33 m  b= 56 m  this is right angle triangle is given  so we can find other side  c2 =a2+b2 c2 =…

Q: QUESTION 14 For f(x, y, z) = x²y-z and F(x, y, z)=xi-xy j + z²k calculate Vf +Vx F.

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Find the derivative of the function. g(u) = Upload u +4 5u+1 Choose a File

A: Given query is to find the derivative of the expression.

Q: Two people start walking from the same point. One walks south at 3 miles per hour and the other…

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Q: iii. S 205x 25x4 dx

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Q: 3. Differentiate a) (x3+2x)e(2x+1) b) cosxsinx

A: Topic = Derivative

Q: I find the limit. Use l'Hospital's Rule where appropiste. If l' Hospital's Role does not, find the…

A: limu→0u+u45-u2

Q: der the following. 5x + y² = 8x Find y' by implicit differentiation. y' = Solve the equation…

A: we will find the required.

Q: Find a function that satisfies the given conditions and sketch its graph. lim f(x)=2, lim f(x) = ∞o,…

A: The function is not defined when x approaches 5 from left or right. So it must be an asymptote and…

Q: D Find the derivative of the function. f(x) = (x³-4)(x+7) Upload Choose a File Question 3 پیار

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Q: Find a polynomial of degree 2 that has two irrational zeros. Explain how you created this…

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Q: 2. Find the average value of f(x, y): 1 over the square In 2 ≤ x ≤ 2 ln 2, In 2 ≤ y ≤ 2 ln 2. xy

A: Here we have to find the average value of a function.

Q: b)lim X118 5x3+x2 3- 15x2

A: Given limit, limx→ -∞ 5x3+x2-23-1.5x2

Q: Consider the equation: |x+1| +5=3x a) Solve to find all potential solutions. b) Verify each…

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Q: Let k(x) = (x + 2)²-5. Find the average rate of change of k(x) between x = -3 and x = 6.

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

Q: 1. Differentiate a) b) x³+4x²+2x-3 2x³−4 x²+3 x³−2 x²+1

A: We know that differentiation power rule is : Differentiate of d(xn)/dx = nxn-1.   Here i attached…

Q: CHAPTER 2 You are the manager of a donut shop. Presently, you sell your donuts for $1.00 each and…

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Q: Find the thos of P(x) = x4 -81

A: To find the zeroes of given polynomial

Q: 4. Identify the equation with a constant of proportionality of 8. 2y = 4x 8y = 8x حدد المعادلة التي…

A: Checking each option as shown below

Q: dy Calculate using implicit differentiation. 증 4 27x=y

A: Given equation:- 27x=y4

Q: Factoring this, we get F(x)=2x3+24x+12x3² + 12x + 6). Since is never 0, then F(x)=0 when x² 12x+6=0,…

A: Given:- f''x=2x-3+24x-4+12x-5

Q: 49. What is the area under the graph of y=f(x)=x²cos(x³) [0, π]. F/N 2 and above the interval…

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Q: Enter the exact answer. To enter √a, type sqrt(a). √x+1-2 lim I-3 I-3 团 Hint: You may want to…

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Q: f(1) = 10 and f'(x) ≥2 for 1 ≤ x ≤ 4, how small can f(4) be?.

A: Given query is to find the value of f(4).

Q: Find the relative maxima and relative minima, if a f(x)=x² - 6x

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Q: need help with number 1. The table to use is attached.

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Q: lim ex x 0x = ex lim x-0 1 LHR = 1 1 = 1. Think carefully about the conditions for l'Hôpital's rule…

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Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 2300 yd…

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: Graph the parabola. y=x²+10x+27 Plot five points on the parabola: the vertex, two points to the left…

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Q: A continuous function y = f(x) is known to be negative at x = 5 and positive at x = 8. Why does the…

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Q: 3. The original price of an item is twice as much as the sale price x. Write an expression for the…

A: Given query is to write the expression for orignal price.

Q: 1. Given the function f(x) = 4x3 + 12x² 15x + 2, a) Find the first derivative and the critical…

A: Given function:- f(x) =4x3 +12x2 -15x + 2

Q: 2. Casey cut an 8-foot board into three sections. Two of the pieces each have length n feet. Write…

A: We can find the length of the third piece.

Q: y = sec ² t 2 y=1-₁² 0 t

A:

Q: maximize the revenue, how many dresses should be made and sold each week? ( hint r(x) =p(x). Round…

A: Given query is to find the value do x which maximize the revenue.

Q: 3x 2 3x -2 3. Consider the following rational equation: + x+1 x+2 x+3 (x+1)(x+2)(x+3) a) List the…

A: Consider the following rational equation: 3xx+1+2x+2-3xx+3=-2x+1x+2x+3a To list the set of…

Q: 127. D = {(x, y) |x² + y² ≤ 4y}

A:

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 77 6 - 1 00…

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