Can you please answer with full solutions?

Without full solutions answer is not useable.

I will be grateful to you for the help.

Thank you so much in advance.

Thanks a lot:)

MATH1005 Introductory Algebra and Calculus MATH1005: Introductory Algebra and Calculus ASSESSMENT . : Calculations Full written solutions must be provided for each question. Final Grade: 25% Question 1 (Module 3) [i) Solve the following system of equations 5c = 1-3d 2d +c+4=0 (a) Using the substitution method (b) Using the elimination method (i) A car is travelling in a straight line with a constant acceleration of a (ms ]. The starting point of the journey is S meters away from the current location, which is given by $ = ut + zat?. where u (ms'] is the initial velocity and c is the time in seconds. (a) Determine the initial velocity i and the constant acceleration a, given that $ = 42 m when [ = 2 s and $ = 144m whent = 4s. (b) Find the new location of the car after 6 s. [ili) The electrical current generated from an electrical circuit can be described by Kirchholl's law, where 6, iz and is represents the currents. Determine the values of 41, 62 and is from following equations. 4+ 82 + 3, = -31 3h - 262 +4 =-5 26 - 362 + 26 = 6[v) Jack invested his savings, a total of $12,000 in a virtual currency platform for Bitcoins, Ethereum and Monero. He received 10 %% profit from Bitcoins, an 8%% profit from Ethereum and 12%% profit from Monero. His total profit was $1230. If the total investments in Bitcoin and Ethereum, equals his Monero investment, how much did he invest in each currency? Question 2 (Module 4, Section 1) [i) Determine the following for the given graph: a. Domain and the range b. x - intercept[s] (if any) c. y - intercept(s) (if any) d. The intervals for which the function is increasing e. The intervals for which the function is decreasing f. The intervals for which the function is constant g. Line of Symmetry h. Vertex of minimum / maximum functional value i. Generate the function of the parabola [ii) Stephen wanted to install a rectangular in-ground swimming pool for his kids. He planned to have a rough tiled sidewalk around the pool with a constant width of : metres. The two outside edges (width and the length] of the proposed sidewalk measures 24 meters by 41 meters. (a) Generate a function of A (x) for the area of the pool as a furiction of x. (b) If the pool area was fixed at 630 square meters, find the width of the sidewalk. (iii) Solve the following equations using logarithmic and exponential laws. (a] log (x - 1) + log (x + 8) = 2 log(x + 2) (b) log(x] -3) - log x = log 2 (c) =log(4) = logx(iv) Jim is a licensed surveyor who works at a high-rise building project. During the final round of inspections, he noticed the angle of elevation of the top of a perpendicular building is 19". Then he moved 120 m nearer to the building and found the angle of the elevation of the same building is now 47'. Determine the height of the building at Jim's worksite into the nearest two decimal places. Question 3 (Module 4, Section 2) (i) Calculate the limits. 3.x -4 (a] lim x-+-1 8r +2x-2 *-1 (b) lim xi x-rtx-1 (c) lim 4-I x-4 5-VX2+9 (ii] Willis tower is 160 meters tall from the ground level. Simon reaches the top of the tower and drops a ball. The height of the ball is given by s(() = - 1602 + 630 where [ is time measured by seconds. Find the average velocity of the ball between the time the ball is released and the time it hits the ground. (iii) Using the formal definition of the derivative, /'(x) = lim I(x+ h) - /(x) h to evaluate the function: (a) / (x) = 2x7 + 3x - 5 atx = - 1 (b) Then prove that / '(0) + 3/ '(-1) = 0 (iv) Two tangent lines can be drawn for / (x) = vx at point (1,1) and (4,2). Find the equations of the tangent lines using the following steps: (a) Determine the derivative of / (x) = vx using method of definition of derivative. (b) Find the slope of the graph at the given points. (c) Generate the equations for tangent lines using the findings above and given data