What are the dimensions of the box

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (et,…

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Q: Consider two positive numbers x and y such that x + y = 58. Maximize and minimize the quantity y…

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Q: why is the 1.20185 squared?

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Q: Use the Laplace transform to solve the given initial-value problem. y" — y' = et cos t, y(0) = 0,…

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Q: A certain vehicle can accelerate from a standing start to a speed of v(t) = -0.27t2 + 14t feet per…

A: To find the formula for distance.

Q: True or False. (SHOW complete proof) d²y 2. tany = C₁ cotx + C₂ is a solution to dx² +2 cotx +2tany…

A: If the given equation is a solution , then it's must satisfy the DE. So we have to use derivative to…

Q: Use the sum-to-product identities to rewrite the following expression as a product.…

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Q: ifferentate: f(x) = COSX 1+sin x Apply the quotient ru

A: Topic:- application of derivatives

Q: Evaluate the line integral foF-dr, where F(x, y, z) = -5 sin azi - 4 cos yj - zzk and C is given by…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Consider the piecewise function f(t) 9t² + 5t + 4 4 cos(5t) 59e4t 5 sin(4t) t 12

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Q: O(fg)' = fg' + gf' O(fg)' = f' + g' O(fg)' = f'g' finding the derivative of the product of two…

A: (fg)' = ? this is the formula of derivative when two function are multiplication (fg)' =f'g +fg'…

Q: Find the measure of the reference angle for each measure of 0. 28) 0 = 165° 29) 0 = -727°

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Q: An open-top box is to be made from a 12-inch by 48-inch piece of plastic by removing a square from…

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Q: why is e and the natural logarithm, rather than other bases, are used in so many situations

A: We have to explain why is natural logarithm is used more.

Q: For each of the differential equations given below, find the general solution using the fol- lowing…

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

Q: Find the area of the largest rectangle that fits into the triangle in quandrant one with sides x =…

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Q: The answer above is NOT correct. Entered [12*(s^2)-27*s+7]/[-4*(s^3)+5*(s^2)-5*s-3] Note: don't…

A: Consider the following differential equation, -4y'''+5y''-5y'-3y=0 with y0=-3, y'0=3, y''0=2.By…

Q: 12 TL² (x+y-z) dz dy dx = 9 Nico 27 8 27 2 A O .BO

A: Option b is correct. This is question based on triple integration.

Q: (a) x² - 4x = -4 (d) e² = 2

A: This question is related to solution of equations, we will solve it using given information.

Q: Explain how you know that the exponential function has an inverse. Knowing the properties of the…

A: Let's check property of given function.

Q: Skeletal remains had lost 81% of the C-14 they originally contained. Determine the approximate age…

A: We want to determine the approximate age (in years) of the bones.

Q: Find f (0) if f(w) 2- ew 1 + ew

A: Givenn function:- fw=2-ew1+ew

Q: Which of the following functions shares no common solution with the function f(x)=-3x²+6x+9 Select…

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Q: The element lithium naturally decays at a continuous exponential rate of 1.9% per month. If a sample…

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Q: the length s of the arc that subtends a central angle of measure 40° in a circle of radius 17 m.…

A: Given query is to find arc length.

Q: Radioactive Decay Phosphorus-32 (P-32) has a half-life of 14.2 days. If 300 g of this substance are…

A: As we know that the radioactive decay is modelled by Q(t)=Q0ekt, where Q0 is the initial amount of…

Q: Hi! Can I have some fraction examples solved? I need an example on "paper" if you can. 5 1/7 - 1…

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Q: Find the value of a so that for f(x) = x³ + ax² − 10x+6 and the interval 0 ≤ x ≤ 4 the location…

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Q: A) f(x, y) = 2x - y². Sketch 4 level curves of f(x, y). B) Evaluate the following limit or show that…

A: In order to find the level curves, f (x, y) = k, where k is a constant. Since we want to draw 4…

Q: Find f(t). f(t) = <{{ e-s s(s+ 1) | +( | ) u(t -|

A: Given:     ℒ-1e-sss+1 Apply inverse transform rule: If      ℒ-1Fs=ft then  ℒ-1e-asFs=?t-aft-a Where…

Q: Find where the line y = 7 - x is closest to the point (0, 0) and then find where the line y = 7 x is…

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Q: (b) Use the gradient to find the directional derivative Du f(x, y) of f(x, y) = 4xy + 3y² at P = (2,…

A: Given: fx,y=4xy+3y2 We know that the gradient is just the vector of partial derivatives.

Q: Calculate the marginal revenue if q = 10. Round your answer to two decimal places. MR = i

A: Topic:- application of derivatives

Q: By carefully showing all your steps, differentiate the function f(x) = (tan−¹(x + √√x)) 4

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Q: Use Theorem 9.11 to determine the convergence or divergence of the p-series 1 1 1 ਲੋਕ · + √3+√4 1 +7

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Q: (4) Suppose z = f(x, y) where f is differentiable (both f, and fy exist). In addition, suppose =…

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Q: Is the graph of g(x) = 4x³ + 9x² + 7x + 3 concave up or down at the point with X-coordinate -2?…

A: g(x)=4x3+9x2+7x+3

Q: Find the directional derivative Du f(x, y) of the function f(x, y) = 6xy² + 3x²2 at the point (-1,2)…

A: Let's find directional derivative at given point and direction.

Q: Consider the function f(x, y) = 3x²+y²-5 x²-2y A. Find and sketch the domain of f. B. Find and…

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Q: Use a trigonometric substitution to calculate a non-zero constant. X √x² + 2ax dx, where a is

A: The given integration is: ∫xx2+2axdx Use a trigonometric substitution to find the value of the given…

Q: Which of the (i) F(x, y) = (10xy+6) i + (9xy+8) j (ii) F(x, y) = (9ye⁹x + cos 6y)i + (x + 6x sin 6y)…

A: We can find whether the field is conservative .

Q: Consider the initial-value problem y(1) = −2. y'-7y=2x, Use Euler's method to obtain an…

A: We need to choose correct option.

Q: Find the solution of the system whose augmented matrix is 0 2 1 1 2 1 0 1 2 1 1200 13 101022 1 0…

A: We have to find the solution of the system whose augmented matrix is 102110101212001101022132

Q: Find all complementary functions of the equation y" -6y' +9y=0. a. cos3x,sin3x b. e-3x.e³x C. e-3x…

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Q: Show that the directional derivative of f(x, y, z) = z²x + y3 at (6, 9, 8) in the direction. √5 To…

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Q: Question 2 > Consider the point P(2,-1,-4) and the vectors a = and b =. (a) Find the unit vector u…

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Q: PROBLEM: Fruit flies are situated in a small glass bottle containing a amount of food. Suppose the…

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Q: n a research experiment, a population of fruit flies is increasing in accordance with the…

A: We know that exponential  growth formula, A=Pekt Where P is initial polpulation t is time k is…

Q: 5. Solve as a linear first-order differential equation: y - 2y = x² +5

A: Solution of linear differential equation y'+P(x)y=Q(x) is given by y×IF=∫(Q×IF) dx+C, where IF=e∫Pdx