The deflection D of a beam of length L is D = 3x4 - 7Lx³ + 2L²x², where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

Q: 10. A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/s. Find:…

A: Given:Initial velocity (v0​) = 128 ft/sAcceleration due to gravity (g) = -32 ft/s² (negative because…

Q: Please find an equation for the line tangent to the graph of y= √x at the point where y = 3

A:

Q: Write the system of linear equations in the form Ax = b. Then use Gaussian elimination to solve this…

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

Q: A vertical container with base area measuring 14 cm by 18 cm is being filled with identical pieces…

A:

Q: find the volume by rotating around the x-axis for f(x)= x/2 and g(x)= sqr(x)

A:

Q: Evaluate the following integral in cylindrical coordinates. 6 √2 √√4-x² SS S 0 0 X 2-y2 dy dx dz 6…

A: We have given an integral We have to evaluate it using cylindrical coordiinate

Q: Find the area of the surface. the helicoid (or spiral ramp) with vector equation r(u, v) = u cos(v)i…

A:

Q: Find the angle between the vectors, approximate your answer to the nearest tenth: v = (-3,-2), w =…

A: The solution is shown in step-2

Q: If x = logę (log₂ 8), y = 2 arccos(1), and z = log4(logg 9), then OI<Z<Y Or<y<z Oy<z<x Oy<x<z Oz<x<Y

A:

Q: what is the relative minimum and maximum of x+1/x^2, x=-2

A:

Q: Consider F and C below. F(x, y, z) = yzex² i + eײj + xye×z k, C: r(t) = (t² + 5)i + (t². (a) Find a…

A:

Q: Find an exponential function of the form P(t)= Pon that models the situation, and then find the…

A:

Q: Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal…

A: Givena = 33, b = 44, c = 21

Q: Solve the given differential equation by undetermined coefficients. y" - y'= -6 y(x) =

A:

Q: Which of the following is an even identity? O tan(8) = sin(e) cos(8) O sec(-8)= sec (0) O csc(-8)=…

A:

Q: lim arctan((z 8118 00 OT/2 =

A:

Q: Write v as a linear combination of u₁, 2, and u3, if possible. (If not possible, ente v = (7, -9,…

A:

Q: 10. A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/s. Find:…

A:

Q: 89°F Partly sunny C If v = 5i+j and w = -5i - j, then the projection of v onto w is: F1 1 O 5i + j O…

A:

Q: 7. A projectile is fired upward from a 15.3 m cliff at a speed of 19.6 m/s and allowed to fall into…

A:

Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. O A = B= C=…

A:

Q: Evaluate the following double integral. J₁ 2² ²+1 ¹² - dA, D = {(x, y)|0 ≤ x ≤ 4,0 ≤ y ≤ √T}.

A:

Q: Consider the following vector field. F(x, y, z) = 3xye²i+yzexk (a) Find the curl of the vector…

A:

Q: Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the…

A:

Q: The vector function r(t)-(26)j + (46² +116) k is parallel to its derivative r(t)- dr/dt when t…

A: We have to find the value of t for which vector function r(t) is parallel to r'(t).If two vectors…

Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyezk, C: r(t) = (t² + 5)i + (t² − 1)j + (t² -…

A: And  ,

Q: ou have the formula y = 3x + 12. Calculate x then y = 45

A: An equation is defined as a statement that shows that two mathematical expressions are equal."Since…

Q: For q (x)= -5x+5x-4 x²+2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the…

A:

Q: True or False: The following problem can not be solved by applying the Law of Sines (AAS): A leaning…

A: Step1

Q: Let b be a positive constant. Find the area of the region bounded by the graphs of f (x) = x2 and…

A:

Q: Consider the rational function g(x) 3x²-5x-2 (i) Factorise the numerator and denominator. (ii) Find…

A:

Q: Use one of the formulas below to find the area under one arch of the cycloid x = t - sin(t), y = 1 -…

A:

Q: Write v as the sum of two vector components if v = i +3j and w = -2i+ 5j. Cloudy ○ v= (¹+¹)+(5¹+5)…

A:

Q: Given that a, b, c, and d are vectors in R³. Is it possible to calculate (à x ¯`). (c · (c + d ) ? ?…

A:

Q: Problem 5. Let f(x)=x² sinx. What is the value of ƒ³ (0) ?

A:

Q: Which is the correct rule to use when converting the complex number z = a + bi to polar coordinates?…

A: The solution is shown in step-2

Q: TC P(t) = 75 cos (1-3)] +725 The function approximates the population, P(t), of rabbits in a nearby…

A:

Q: by completing the following: (a) Partition the interval [a, b] into n subintervals of equal width Az…

A:

Q: If f(x) = eV/2, then f-¹ (2) is O3 log2 ○ 2(lnx)³ ○ 3(In x)² O the inverse does not exist O2 logg

A:

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) =…

A: The given function is,

Q: 9) 11. 13. od 15. 17. 5 19. 64 dx 20/19 8 dx 13 (x +413/2 -3 dx √4-x L'₁ 21. 23. 3 dx -3x f.ro - ds…

A:

Q: 2x If ƒ (x) = e²x (x³ + 1), then ƒ¹ (2) =

A: If , then to determine .

Q: Determine which set of vectors is orthogonal. O v = (-3,1), w = (1,3) v = (0, -2), w = (0,³) O O v =…

A:

Q: Determine whether the matrix is orthogonal. P = 2 I ~/3 2/3 ~/3 ا ~/31/32/3 ~/3 ~/3 N/M 2 1 12 2 3

A:

Q: F2 Determine if the following set of vectors is orthogonal. Explain why or why not. v = (16,-8), w =…

A:

Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A:

Q: (a) f(x) = (x¹/2+2-1/2) √In(x)

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. A = 47°, b =…

A: Given , In a triangle ABC

Q: Find the vector that is orthogonal to the projection vector that comprises the sum of two vector…

A: The projection vector p of vector v onto vector w is given by ..........(1)Now,

Q: 32. f(cotx - tan x)² dx

A: