In a class of 27 learners, what is the probability that at least two learners share the same birthday?

Q: 3. DETAILS TANAPCALC10 2.4.076. 0/2 Submissions Used Find the indicated limit, if it exists. (If an…

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Q: Question #9 to the function The Population of Palatine is growing exponentially according…

A: According  to question,Given function,Pt = 37 e0.015t

Q: 2. The temperature of a point on the sphere x2 + y² + z2 = 9 is given by T(x, y, z) = x+y+4z. We…

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Q: This question is about plotting two points and drawing the straight line through them. Which TWO…

A: The equation of line y=-6x+2

Q: Determine whether the series converges or diverges. 8n n² + 1 The series converges. O The series…

A: To determine whether the following series converges or diverges. ∑n=1∞ 8nn2+1 To determine the…

Q: Suppose the straight lines L₁ and L₂ have respective vector equations 4 5 9 -5 (99)-0) -3 +t = -…

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Q: Simplify. −x²³y² − 4x²y² + xy² -7x³y² +5x² - 2x³y² O-9x³y2²-4x²y² + 5xy² O-14x³y²-4x²y² + 5xy²…

A: Simplify

Q: *30 A table of values of an increasing function f is shown. Use the table to find lower and upper…

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Q: Question 2.7d. Consider the linear system of differential equations 4x - 6y y' = 2x - 4y Select the…

A: The given equations are;  x'=4x-6y y'=2x-4y x(0)=0, y(0)=1

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: The acceleration of a particle is a→t=<5t, 3 sint, cos3t>. The initial conditions, v→0=<0,…

Q: 30. p = V 2x 500 - x 2x 0 < x≤ 500

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Q: Find the critical point of the function f(x, y) = − (16x + 4y² + ln(|x + y))). C = Use the Second…

A: To find the critical point of the function fx, y=-16x+4y2+lnx+y. By using the second derivative test…

Q: In each of Problems 8 through 11, use the linearity of the Laplace transform to find the Laplace…

A: Use the linearity of the Laplace transform to find the Laplace transform of the given function; a…

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: a · b = |a| |b| cos(θ), where a · b is the dot product of vectors a and b, |a| and |b| are the…

Q: Given the expression below. a) Show the given values of the cosine function on the right triangle.…

A: cosθ=1415

Q: Fill in each box below with an integer or a reduced fraction. (a) log₂ 8 = 3 can be written in the…

A: To fill in each box with an integer or a reduced fraction. (a) log2 8=3 can be written in the form…

Q: Can anyone show me a full solution for this calculus word problem? Can you please write in…

A: It is given that we have rectangular field.

Q: Question #1 -Let the revenue of a refrigerator be given by the equation R(x)=280x-0.4x² x = number…

A: Given:  Let the revenue of a refrigerator be given by the equation,  Rx=280x-0.4x2 where, x=number…

Q: Solve the initial value problem. xy'+y = x² + 4, y(1) = 5

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Q: 2. The temperature of a point on the sphere x² + y² + z² = 9 is given by T(x, y, z) = x+y+4z. We…

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Q: (1) Sketch the region of integration and change the order of integration of do not solve the…

A: To sketch the region of integration and to change the order of integration. (a) ∫14∫x-22x fx, y dy…

Q: 1) Solve the following differential equations a) y'=x¹/²(y+y¹/2) b) ty+y=t¹/2

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Q: 85 n=0 400

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Q: Ex.16 Please answer clearly

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Q: Q5 F(x) = x² + 1 is an antiderivative of what function: (a) f(x) = x³ +C (b) f(x) = 2x (c) f(x) = x³…

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Q: r² Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: Use the shell method to find the volume of the solid generated when the region bounded by: y=(1+x²)…

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Q: 22. C = 100(9 + 3√x)

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Q: -5 -4 -3 4 The above is the graph of the derivative f '(x). How many critical points does the…

A: We know that critical point 'x' of any function f(x) is where the derivative of f(x) which is f'(x)…

Q: Suppose that a pencil holder is in the shape of a right circular cylinder, which is open at one of…

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Q: Find a unit vector that has the same direction as the given vector. -6i+4j - k

A: Given vector, - 6i + 4j - k

Q: Physicians often treat thyroid cancer with a radioactive form of iodine called iodine-131 (1311).…

A: For a patient treated with 125 mCi (millicuries) of I131, the radioactive level  R (in mCi) after t…

Q: Use the method of undertermined coefficients to find the general solution of the differential…

A: We use methods of higher order linear differential equations to solve the given differential…

Q: The function f(x) = -2x³ +39x² 240x + 4 has one local minimum and one local maximum. This function…

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Q: The function f(x) = 2x³ − 42x² + 240x-2 has two critical numbers. The smaller one is x = and the…

A: given function is f(x)=2x3-42x2+240x-2

Q: 7. The surface area of a cylinder is given by the formula SA = 2лr²+2лrh, where r represents the…

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Q: tan (0) Rewrite the expression esc(0)sec(0) in terms of one trigonometric function

A: let G=tan(θ)csc(θ)sec(θ)

Q: 6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1).…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 8 sin(t). The initial…

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Q: let S = {1-¹ | neN}. Show that sup S = 1. Hint: Use also the AP.

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Q: Let A = (1, -2, 2), B = (0, -1, 3), and C = (2,c4, c), where c is a real-valued constant. Find all…

A: Let A=(1, -2, 2), B=(0, -1, 3), and C=(2, c-4, c) where c is a real valued constant.

Q: a) f(x) = (5x² + 4) (2x²-3x) b) f(z

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Q: To find the blue shaded area above, we would calculate: b [ f(x) dx = area Where: a 1 f(x) ■ Area ■…

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Q: Find the scalar and vector projections of b onto a. a = (-1, 4, 8), b = (18, 2, 1) scalar projection…

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Q: Question #9 to the function The Population of Palatine is growing exponentially according…

A: Pt=37e0.015tHere t is the number of years since 1950 ,Pt is measured in 1000's of people

Q: True or False? Vector functions r 1 = ti + t 2 j, 0 ≤ t ≤ 1 , and r 2 =(1 — t )i+(1 — t ) 2 j, 0 ≤ t…

A: Given: Vector functions: r1=ti+t2j, 0≤t≤1r2=(1-t)i+(1-t)2j, 0≤t≤1 We are required to find: If the…

Q: O Find the parametric equation of a plane through the points (1,0,0), (0, 0, 1) and (1, 1, -1).

A: To find the parametric equation of a plane through the points 1, 0, 0, 0, 0, 1 and 1, 1, -1.

Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

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Q: The total revenue for Dante's Villas is given as the function R(x) = 500x -0.5x², where x is the…

A: NOTE: Refresh your page if you can't see any equations. . the revenue function is given by where x…

Q: The force on a particle is described by 8x³ - 2 at a point x along the x-axis. Find the work done in…

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