Math Answers

Find the local and absolute extreme values of the function on the given interval. Also

specify the intervals where function is increasing or decreasing

(i) 𝑓(𝑥) = (𝑥²+ 𝑥 + 1)²

Q: Find the local and absolute extreme values of the function on the given interval. Also

specify the intervals where function is increasing or decreasing

𝑓(𝑥) = 𝑥²e^-x

6. In the manufacture of car tyres, a particular production process is know to yield 10 tyres 

with defective walls in every batch of 100 tyres produced. From a production batch of 100 tyres, a sample of 4 is selected for testing to destruction. Find: 

i) the probability that the sample contains 1 defective tyre. (ii) the expectation of the number of defectives in samples of size 4. (iii) the variance of the number of defectives in samples of size 4.

5. A person who wants to get a driving license, has to face two separate tests. Road test is the one of these two tests and there is a 0.75 probability that an application for a drivers license will pass the road test on any given try. 

i) What is the probability that an applicant will pass the road test on any given try? 

5. A person who wants to get a driving license, has to face two separate tests. Road test is the one of these two tests and there is a 0.75 probability that an application for a drivers license will pass the road test on any given try. 

i) What is the probability that an applicant will pass the road test on any given try? 

P(-4.80 z 3.54

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).

The recipe for mint chocolate ice cream requires 2 and half cups of cream for 10 people.You need ice cream for 16 people.How much cream will you need?

Hannah made a bank loan worth Php 200,550 with 5% interest compounded semi-annually (2 times in a year). If she is to pay at the end of the period only, how much will be the value of the loan after 2 years?

A delivery company accepts only rectangular boxes the sum of whose length and the perimeter of a cross-section does not exceed 108 inches. Find the dimensions of an acceptable box of largest volume.