6) (10 pts) Calculate a) sin(8 +81) b) sinh(7 + 75)
(1 point) Since 8t2 sinh(at) + 5+ sin(at) = ť? (8 sinh(at) + 5 sin(at)). to find the Laplace transform of 8t? sinh(at) + 5tsin(at) you take the second derivative of Therefore L{8t2 sinh(at) + 5t2 sin(at)}(s) =
Find the derivative of the following: f(x)=( Sinh(Sin-(x2)))3 оа. Select one: - 6X(Sinh(Sin-(x^))) Cosh(Sin-1(xº) √1-8" 3(Sinh(Sin-'(x2)))?Cosh(Sin-'(x2)) O b. 71-X 3(Sinh(Sin '(x2))) Cosh(Sin ?(X)) O c. 71-X 6XCosh(Sin-'(x?)) O d. V1-14
5. Evaluate the following differentials (a) det? (b) d sinh ở (c) dx sin (d) do y 6. Find the exact values of the following expressions. Justify your answers using the definitions of they hyperbolic functions. (a) sinh (In 3) (b) cosh (In 3) (c) tanh (In 3) 7. Suppose cos 2 + siny = 1 (a) Use implicit differentiation to find y' = dy. Simplify your answer as appropriate. (b) Use implicit differentiation to find y" dy. Simplify your...
Add the two vectors: A = 41+ 7j and B = 81 - 9j 10 11i - 1; 12i +2j 121 - 2j Question 6 What is the magnitude of the vector 7A, where A = 8i+-2.
all parts please PART II 7) (8 pts) Given the polar equation r = 6 sin θ, 0 θ π a) Graph and find the length of the graph geometrically. b) Find the length of the graph by integrating. 8.) (9 pts) Given the four-leaved rose r 2sin(26). a) Show the symmetries. b) Find the tangents of the leaf through the pole to determine the limits of integration. c) Find the area of one leaf. PART II 7) (8 pts)...
4. (12 pts) Find the exact value of sin(a + b) if sin(a) = B in quadrant I. and sin(B) = 5, with a in quadrant III and
D5.5. Given the potential field in free space, V 100 sinh 5x sin 5y V, and a point P(0.1, 0.2, 0.3). find at P: (a) V: (b) E: (c) El: (d) Ipsl if it is known that P lies on a conductor surface. Ans. 43.8 V,-474ax 140.8ay V/m; 495 Vm; 4.38 nC/m2
question 10 and 11 10. Solve the equation 5 cosh x – 3 sinh x = 5. 11. (a) Show that cosh (x - y) = cosh x cosh y - sinh x sinh y. (b) Show that for any real number x, cosh” x + sinh? x = cosh2x . Hence prove that cosh2x = 2 sinhạ x + 1 = 2 cosh? x - 1. 1+ tanh x (c) Show that 1- tanh x
5. (20 pts.) Given: sin a = 3/5 and sin B = 5/13. Where a is in Quadrant II and B is in Quadrant I. Determine the following and report all numerical answers in exact form. a. (02 pts.) Construct both b. (03 pts.) cos a C. (03 pts.) cos Right Triangles d. (02 pts.) sin(a + b) e. (02 pts.) cos(a + b) f. (02 pts.) tan(a + b) g. (02 pts.) sin(a - b) h. (02 pts.) cos(a...