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- Suppose z is a complex number, where z = x+iy then: a. Re(z)=(z+z°)/2 b. Re(z)=(z.z')/3 O c. Re(Z)=(z-z')/4 d. Re(z)=z-z*ipa Suppose (p | ) = e¯. What is (x | b) =? V2nh 8 (x – x') 2nh Vasi 8 (x – x') 2πh 8 (x – x') O O1%A9 li. t LTET 4G+ Vol) O A X O U 9:-7 Second H.W.pdf 1. Draw and label the vector with these components. Then determine the magnitude and angle of the vector. a- Az = 3 ,A, = -2 b- B, = -2 ,B, = 2 2. What is the speed of horse in meter per second that runs a distance of 1.2 miles in 2.4 minutes? 3. A car moving along X- axis according on the function: X (t) = 2 t2 + 5t +7 on [1,2] Find: a- The average velocity. b- The acceleration at 3s. 4. Julie is walking around a track at a 2m/s for some exercise. She then decides to start jogging so she accelerates at a rate of 0.5m/s? for 3 seconds. How far did Julie travel from the time she started to accelerate to the end of the 3 seconds? 5. Ralph uses a 2000 to do this. force to push his car along a road for 1000 m. It takes him500 s a- Calculate the amount of work that Ralph did on the car. b- Calculate the amount of power that he generated. II
- The continuity equation satisfied by u = 4xy+y?, v= 6xy+ 3y 10 u= 3x^2-2y^2, v=-6xy .II O u=x-4y, v=y-4x .IIIO10.4.77 Two forces of magnitude 40 newtons (N) and 20 N act on an object at angles of 30° and -45° with the positive x-axis as shown in the figure. Find the direction and magnitude of the resultant force; that is, find F1 +F2- F|-4 = 40 N 30° - 45 I|Fl = 20 N F1 +F2 = (48.78) i+ (5.86) j (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)The angle between the vectors that connect ther carbon atom to the hydrogen atoms in the methane molecule can be calculated using the dot product or the cross product rule. In the case of the dot product, we get the correct answer, which is 109.5 degree, but if we use the cross product, the answer might be 70.5 degree. Why?
- Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The num- ber after t hours is shown in the accompanying figure. 250 200 150 100 50 0 1 2 3 4 5 6 7 a. Explain what is meant by the derivative P'(5). What are its units? b. Which is larger, P'(2) or P'(3)? Give a reason for your answer. c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by P(t) = 6.10r2 – 9.28t + 16.43. Find the instantaneous rate of growth when t = 5 hours.Which of the following equations repreşents a power relationship? Select one: C =8+0.016 a. O b. N=14e0.01t O c. y = 3x-1 d. V =10t+3 %3D С. %3DPerform the following arithmetic operations, keeping the correct number of significant figures in your answer. a. The product 56.2 0.154 b. The sum 9.8 + 43.4 + 124 c. The quotient 81.340/
- A vector field is defined by: F (x,y,z) = -xi - yj + zk Select the option that gives F expressed in cylindrical coordinates. A. F (r,ø,z) = -reø + zezB. F (r,ø,z) = (-x cos ø - y sin ø) er + (x sin ø - y cos ø) eø + zez C. F (r,ø,z) = - rer + zez D. F (r,ø,z) = reø + zez E. F (r,ø,z) = (x sin ø - y cos ø) er + (-x cos ø - y sin ø) eø + zez5. Bir F = (2î+ 3j)N kuvveti z-ekseni boyunca uzanan sabit bir eksen etrafında dönebilen bir cisme uygulanıyor. Kuvvet, ř = (4î + 5j)m noktasına uygulanırsa, z-eksenine göre net torku ve büyüklüğünü hulunuz.Q 1: Let å = -2 ỉ +3 j +6 k and b = 4 i + 6 j , Find ( 2 å + 3 b ,1-ål, å * å , å * b_ )