Math Answers

Find the last three digits of the number 3×7×11×· · ·×2003. [Hint: Chinese

remainder theorem.]

Given that U

 is a function of x,y

 and z

 and A

 a vector field, prove that:

∇×(UA)=(∇U)×A+U(∇×A).

Based on the relative frequency histogram below, which of the following statements is supported by the plot?

The following table displays the mathematics test scores for a random sample of, along with their final SY16C grades.

a.Fit the regression line y=a+bx to the data

and interpret the results.

b.Use the regression equation to determine the SY16C grade for a college student who scored 60 on their achievement test. What would their SY16C grade be?

Mathematics (x)SY16C grade (y)139652437832152464825579264789728738759893456

Noel, a 35 year old office worker, has been struggling with his weight for a long time. He is looking to start dating again, so earlier this year he decided to join a gym. A few days ago he noted that his average weight for the past 6 months is 220.6lbs and the standard deviation is 96. He is hoping that his weight will be between 160lbs and 180lbs by the end of January.

What is the probability that he will achieve the weight he desires? Interpret your result 

1.  y'' + 4y' + 7y = 0         ans, y= e^-2x(c₁cos"sqr3" x+c₂sin"sqr3" x)

Find out the value of an investment that will give you Tk. 60,000 per year forever with a

discount rate of 14% compounded quarterly.

1.  y'''-4y'=0                   ans, y=c₁+c₂e^2x+c₃e^-2x
2. y'' + 9y' + 5y = 0 

1. y'''+3y''+4y'-8y=0    ans, y= c₁e^x+e^-2x(c₂cos2x+c₃sin2x)
2.  y⁽⁴⁾-4y''=0                   ans, y=c₁+c₂x+c₃e^2x+c₄e^-2x

1.  y⁽⁴⁾+8y''+16y=0       ans, y=(c₁+c₂x)cos2x+(c₃+c₄x)sin2x
2. y⁽⁴⁾+4y''+4y=0          ans, y=(c₁+c₂x)cos "sqr2" x+(c₃+c₄x)sin"sqr2" x