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- If In(x) 3.37, what is the value of x?Step 1 Rewrite the original integral Therefore, let du a² + u² (²) dt as + 16 = arctan(y) to Step 2 Use the following integration formula for the inverse trigonometric functions. 1.20 t (27²2² +42 (2) ot = (- t 1 + X X 4 2 (2) dt arctant arctan tan()+c 4 ✓)) + CDetermine the values of I, and 1, that satisfy the following two equations. 8.15 + 3.40/, - 2.1012 = 0 and -2.10/, + 12 = 0. (a) 1= A (b) 12 = A Need Help? Read It
- Question 2 Pauli matrices are important in physics. They are: (: :). - 1 0 -i Ox = 1 0 Oy = i 0z = Now consider a vector where 0 is a number and în is a unit vector. Now consider the following matrix: P = ng0x + nyơy + nz0z. Prove that: I2 for k even, P for k odd. 1 Now consider the following matrix exponential: (i0P)™ m! m=0 Show that = I, cos 0 + iP sin 0 . Hint: You may find these two formulas useful: (-1)° 0²p Σ (2p)! (-1)º 0²p+1 sin 0 = Σ cos 0 = (2р + 1)! p=0 p=010 3.1.P.001 Two points in the xy plane have Cartesian coordinates (3.50, -5.00) m and (-6.50, 6.50) m. (a) Determine the distance between these points. 14.60 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your c four-digit accuracy to minimize roundoff error. m (b) Determine their polar coordinates. (3.50, –5.00) r= 6.10 (3.50, -5.00) 8 = -55 O counterclockwise from the +x-axis (-6,50, 6.50) r = 9.19 m (-6.50, 6.50) ° counterclockwise from the +x-axis Need Help? Read It Viewing Saved Work Revert to Last Response Submit Answer Type here to searchUse Excel to evaluate the following equation: y = 33 28 Hitung fungsi y tepat kepada 8 titik perpuluhan. Compute the function y precise to 8 decimal places. 34 29 35 30
- 4. Find all second order derivatives for the following functions. (a) f(x,y) = 2.x2 + 3xy + 2y?, (b) f(x,y) =sin (x- 2y).w = FjAc = F .Aë , W = m(v;)* - m(u,)* , v 1 zm(us)* - m(v,)* , W = Problem 1: (a) à = 3â – 2ŷ, B = 4â& – 5ŷ. à ·B =? Answer: 22 (b) à = -2â + 4ŷ, B = 3âu – lŷ. Ā·B =? Answer: –10 (c) à = 5â – 3ŷ, B = -3â – 5ŷ. ÷B =? Answer: 0 1 | F,dx , W = F. dř , F, dU W = -AU dx d = 4m F = 20 N 0 = 30° m = 4 kg Hk = 0.5) m = 2 kg F = 40 N Hk = 0.2 Ө — 30° Problem 2: In the figure above on the left we have a force F = 20 N pulling a box to the right at an angle 0 = 30° above the horizontal. The box has a mass m = 2 kg, the coefficient of kinetic firction between the box and the ground is uk = 0.2, and the block moves a distance d = 4 m to the right. (a) What is the work done by the force F? Answer: 69.3 J (b) What is the normal force from the ground? Use g = 10 m/sec² Answer: 10 N (c) What is the work done by the kinetic friction force? Answer: -8 J (d) What is Wnet, the net work done on the box? Answer: 61.3 J (e) The box has an initial speed of 4 m/sec. What is the speed of the box after it has…Hi, I got 1.270 as my answer. Could you please double check your answer? I did, 1/sin(52) = 1.270