There are 25 points on the plane and there are no three points on the same straight line. How many triangles are defined by these points?

Q: Solve the following differential equation:   y'' + y' - 2y = 0

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Q: Determine the solution xy³ dx + ye of the 1st Ordered Differential Equatio *dy = e*dy

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Q: (b) lim √√9x-11 -4 X-3

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Q: Now using L'Hospital rule evaluate the following: sin x tan x a) lim x →0 x³ b) Evaluate the limit…

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Q: Q₁. Find the angle between every two vectors below ( Vote b) f-3i+2k and g=4i+4j-2k

A: In this question, we need to find the angle between two vectors.

Q: 2) lim x→4 4x-x² 2-√√x

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Q: 15-16 Find the domain of each function. 1 - et² 15. (a) f(x) (b) f(x

A: Please refer to the image below

Q: 3 Calculator active. Line L is tangent to the graph of y = 2 sin x at the point (k, 2 sin k), where…

A: Equation of tangent line L of a curve y=f(x)  at a point (a,b) is given byy-f(b)=f'(a)(x-a)

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Q: Sketch the graph of a function f for which f(0) = 0, f'(0) = 3, f'(1) = 0, and f'(2) = -1. y y -1 -1…

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Q: If P(x) = 5x – 7, Q(x) = 3x² + 5x + 6, and R(x) = 7x² + 6, find the following: (a) R(x) + Q(x) = (b)…

A: I have solved step by step in detail...go through the solution

Q: Precalculus   Find an equation of the circle with center (2, 5) that passes through (−3, 1).

A: Given query is to find the equation of the circle.

Q: Using the attatched equation 3.9, find the general solution of the following differential equation…

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Q: 9. Figure shows a container for water, ABCDEF, in the shape of a triangular prism. The cross-…

A: The given figure is shown below: A few more vertices were introduced in this figure.

Q: B. 10/3 square units

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Q: Consider the following graph of y = f(x): s What is the lim fx f(x) x-0 A.0 B. 1 OC. -1 D. 2 E. The…

A: From the graph we can see that as x tends to 0, f(x) tends to 1.

Q: (d) t³y + 4t²y=et, (e) ty' + (t+1)y=t, y(-1) = 0, -1≤t<0 y(ln 2) = 1

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Q: - Two forces are applied to the construction bracket as shown. F₁ = 800 lb and F2 410 lb, and their…

A: Topic- vectors We are givenF1=800lbF2=410lbangle F1makes with x axis=70°angle F2makes with x axis=θ°…

Q: Evaluate lim A. dne 3x³-4x²+1 A. R x-00-7x³+x2+2 B. 0 C. - 31/12 The domain of y = log(1-2x) is B.…

A: Givenlimx→∞3x5-4x2+1-7x5+x2+2 We have to find the value of the limit of the function And we have to…

Q: 2. Consider S: x¹e² − yz² + xy = 0, where z is a differentiable function of the - two independent…

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Q: 1. Pirkko wants to invest 9 000 euros so that after 8 years she will have 14 000 euros. What is the…

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Q: y" + 4y = sec²2x

A: Given: y'' +4y=sec22x The general solution of the corresponding homogeneous solution is y=c1 cos…

Q: 12-14 Simplify the expression. 12. tan(sin ¹x) 13. sin(tan ¹x) 14. sin(2 arccos x)

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Q: A salesman sold ​$300 more than the rest of the sales staff. If the sales total for the day was…

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Q: Solve the following Be dy = y(xy ²³-1) dx

A: The given differential equation is; dy/dx=y(xy3-1) Repost the next question.

Q: Q4 Find function's domain, function's range, and determine if the domain is an open or closed region…

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Q: dz dt 2 Find where z = 3x²y3³, x = t4 and y = t²

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Q: Find the difference quotient (z+h)-f(z) for the function given below. f(x) 1²+1+2 Give a simplified…

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Q: 9) A rectangle has one corner on the graph of the line y = -x² + 6, another at the origin, a third…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: EXAMPLES Find an equation of the tangent line to the parabola y--&x+9 at the point (2.-3). SOLUTION…

A: Find equation of tangent line

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

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Q: Determine the interval (s) on which the vector-valued function r(t)=ti+(sqrtt+1j)+(t^2+1)k…

A: The answer is given below:

Q: 3.  Evaluate the integral. (If the quantity diverges, enter DIVERGES.) 3 0 1 9 − x2  dx…

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Q: A. g(x) is increasing at x = -7 3. g(x) has a relative minimum at x = -7 C. g(x) is decreasing at x…

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Q: Find the equation of the plane passing through the points O=(0,0,0), A=(−4,5,1)and B=(−1,0,−6)

A: plane passing through the points O=(0,0,0), A=(−4,5,1)and B=(−1,0,−6)   that is plane passing…

Q: Iculate zu for z=₁₁₁x = e Z X 2u cos(3v), y = e²usin(=

A: We are given  z=2x-yx+3y, x=e2ucos3v, y=e2usin3v we have to evaluate zu=∂z∂u

Q: In problems 19-28, represent each repeating decimal as a series using the sigma notation. 19.…

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Q: QUESTION 3 Derive a Differential Equation that is free from arbitrary const

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Q: Solve for the partial Derivaties of each equations

A: We have to solve for partial derivatives (1) f(x, y) = x4 + 6√y - 10

Q: hello please help in assisting me with how to get the functions for this shape

A: NOTE: Refresh your page if you can't see any equations. .

Q: 51-52 Find an equation of the tangent line to the curve at the given point. 51. y = e* cos x + sin…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 14. Find a y=r³ parametrization for the path that travels along the graph of z from (-1,0) to (1,0).

A: To find the parametrization of the path that travels along the graph of y=x3-x from (-1,0) to (1,0).

Q: Let h(x) = tan (2). Which of the following best describes its fundamental algebraic structure? A. A…

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Q: Sketch the region bounded by the paraboloids z = x² + y² and z= 32-x² - y².

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Q: The chord of the arc subtended by 5°03'25" will vary in length with the radius. Which of the…

A: Sketch the schematic diagram of given question.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) √er (5 + 6e 6e)7/2 dr

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