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A) If you get a slice of pizza with perimeter 90cm,what will be the diameter of the pizza for you to have gotten the largest pizza?



B)A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y -coordinate of P. What is the equation of the curve?


1.      What is the core discussion of the Keynesian cross?

 

2.      Why are actual and planned expenditure simultaneously analysed?

 

3.      Why is the multiplier effect taken into consideration in the Keynesian cross?

 

4.      How does the Keynesian cross model, explains, the functions of Fiscal policy?

 

5.      Why are MPC and the ΔG critical variables in the multiplier effect?


Consider the curve y= f(x) for the function f(x)=e^2x-x^2

a)identify the domain of f

b)Find x,y-intercept

c)find the first and second derivatives

d)the critical points of the function f

e)where is the curve decreasing and increasing

F)find the point of inflection if any and discuss the concavity of the curve

G)Identify any asymptotes



A shipment of 12 Apple mobile phones contains 3 defective phones. In how many ways can a store purchase 5 of these phones and receive at least 2 defective phones?

If the number is only divisible by 3, print "Fizz"


If the number is only divisible by 5, print "Buzz"


If the number is divisible by both 3 and 5, print "FizzBuzz"


If nothing is true in the previous conditions, skip the number

Input two integers in one line. The first inputted integer will be the starting point, and the second one shall serve as the ending point.


Use the power of loops to loop through the starting point until the ending point (inclusive), and print out each number within the range with the corresponding format shown on the sample output. However, skip the printing of statement if the integer is divisible by 4. Tip: Utilize the continue keyword to complete the process

The owner of a factory that sells a particular bottled fruit juice claims the the average capacity of their product is 250 ml to the test claim a consumer group gets a sample of 100 such bottles calculates the capacity of each bottle and then finds the mean capacity to the be 248ml.The standard deviation is 5ml . Test the hypothesis that the population mean is less that 250 ml. Assumed that the population is normally distributed. Use level of significance level is 0.5 and the z value is 1.645


Print out the cube values of the numbers ranging from 1 to 20 (inclusive). However, if the number is divisible by either 3 or 5, do not include them in printing and proceed with the next numbers. Tip: When skipping through special values, make use of the keyword continue and put them inside a conditional statement.

Two spheres of equal mass and equal charge are separated at a distance r.


(a) Derive an expression for the quantity of charge that must b on each sphere so that the spheres are in an equilibrium where attractive and repulsive forces are balanced.


(b)How would doubling the distance between spheres affect the expression for the value of q from the previous problem. Explain.


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