Math Answers

{F} The equation for a displacement 𝑠(𝑚), at a time 𝑡(𝑠) by an object starting at a displacement of 𝑠0 (𝑚), with an initial velocity 𝑢(𝑚𝑠 −1 ) and uniform acceleration 𝑎(𝑚𝑠 −2 ) is: 𝑠 = 𝑠0 + 𝑢𝑡 + 1 2 𝑎𝑡 2 A projectile is launched from a cliff with 𝑠0 = 30 𝑚, 𝑢 = 55 𝑚𝑠 −1 and 𝑎 = −10 𝑚𝑠 −2 . The tasks are to: a) Plot a graph of distance (𝑠) vs time (𝑡) for the first 10s of motion. b) Determine the gradient of the graph at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. c) Differentiate the equation to find the functions for: i) Velocity (𝑣 = 𝑑𝑠 𝑑𝑡) ii) Acceleration (𝑎 = 𝑑𝑣 𝑑𝑡 = 𝑑 2 𝑠 𝑑𝑡2 ) d) Use your results from part c to calculate the velocity at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. e) Compare your results for part b) and part d). f) Find the turning point of the equation for the displacement 𝑠 and using the second derivative verify whether it is a maximum, minimum or point of inflection. g) Compare your results from f) with the graph you produced in a).

Let F(x,y)=2x^2+3sin y and let G(x,y)=e^x-2y.Compute the Jacobian determinant d(F ,G)/d(x,y)

Construct the probability distribution for each random variable X.

a. The random variable X represents the number of heads that occur when you toss 4 coins at the same time.

b. The random variable X represents the number of male children in a 3-child family.

c. The random variable X represents the amount gain by a person who buys s 20 peso ticket from a total of 1000 tickets for a raffle whose winner will obtain ₱5,000

Construct the probability distribution for each random variable X when The random variable X represents the amount gain by a person who buys s 20 peso ticket from a total of 1000 tickets for a raffle whose winner will obtain ₱5,000

. You open a checking account. You are paid 3% interest on the average balance but are charged a 7 monthly charge. Assuming that interest is paid monthly regardless of the number of days in the month, calculate the average daily balance you must maintain to offset the 7 monthly charge.

To make a certain household paint, you need to mix 3/4L of white paint, 15ml of red paint and 10ml of yellow paint. If you need a total volume of 31 litres of this paint, how much of each colour must you mix?

Six professor begin courses on Monday, Tuesday, Wednesday, Thursday, friday, and Saturday, and announce their intention of lecturing at interval of 3,2,5,6,1and 4 days respectively the regulations of the university forbid Sunday a lecture(so that a Sunday a lecture must be omitted) when first will all six professors find themselves compelled to omit a lecture

what is the centroid of x^2=y, x+y=6, x=0. with solution

Y=c1e^x+c2e^2x y"-2y+3y=0

The coordinates of the image of 𝑃(𝑥, 𝑦) when 𝑦 = 𝑓(𝑥) is transformed to

𝑦 = 2 𝑓(𝑥 − 3) − 1 are 𝑃′

(2, 3). Find the original point (𝑥, 𝑦).