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Vectors intersection question:
A line can either lie on a plane, lie parallel to it or intersect it.
Determine, if there is one, the point of intersection between the line given by the equation:
x-5/2= y-1/-1 = z-15/4 and the plane given by the equation:
[x,y,z]= [-2,-7,5]+ s[2,6,3]+ t[1,4,-1]
b)Determine the angle between the line and the plane.
c)Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane.
A line can either lie on a plane, lie parallel to it or intersect it.
Determine, if there is one, the point of intersection between the line given by the equation:
x-5/2= y-1/-1 = z-15/4 and the plane given by the equation:
[x,y,z]= [-2,-7,5]+ s[2,6,3]+ t[1,4,-1]
b)Determine the angle between the line and the plane.
c)Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane.
use the formula cosQ=1/2(e^iQ+e^-iQ) to obtain the identity cos^5 Q=1/16(cos5Q+5cos3Q+10cosQ).
solve the equation z^4=-2 sqrt3 - 2i. Sketch the solutions in the complex plane.
Find in its simples form the quadratic equation with the pair of solution 1/2 ± 3i
The Taylor series about 0 for the function f(x)=1/(1-x) is 1+x+x^2+x^3+x^4+x^5+...use this to find Taylor series for 1/(1-x^3), giving the first 3 non-zero terms.
A)Solve the following simultaneous inequalities
8x - 3≤ 1/4 [x + 16]< x + 10
B) Differentiate the following functions
y = x^3+〖6x〗^(-4)-〖4x〗^(1/2)+ 10
y = (〖6x〗^3+〖4x〗^2+3)(〖2x〗^2-〖4x〗^(-2)+5)
8x - 3≤ 1/4 [x + 16]< x + 10
B) Differentiate the following functions
y = x^3+〖6x〗^(-4)-〖4x〗^(1/2)+ 10
y = (〖6x〗^3+〖4x〗^2+3)(〖2x〗^2-〖4x〗^(-2)+5)
Find the Derivative of y=x^2e^(-3x)
a)use the binomial series to find the Taylor series about 0 for the function f(x)=(1+x)^-1/5, giving all terms up to the one in x^4, and calculating each coefficient as an integer or a fraction.
b)state an interval of validity for this series.
c)use this series and the Taylor series for cosx to find the cubic Taylor polynomial about 0 for the function f(x)= cosx/(1+x)^1/5.
b)state an interval of validity for this series.
c)use this series and the Taylor series for cosx to find the cubic Taylor polynomial about 0 for the function f(x)= cosx/(1+x)^1/5.
You decide to conduct your own investigation based on your team’s performance after their first 10 games of the season. The result of your assessment is found in the table below.
Game: 1 2 3 4 5 6 7 8 9 10
Shots (x): 25 38 43 32 36 23 30 45 46 37
Goals (y): 3 5 7 5 4 0 3 4 4 3
a. Find the linear equation of regression for the line of best fit.
b. Compute the correlation coefficient (r).
c. Estimate the number of shots that would be needed in order to score 8 goals.
d. If it is known that 43 shots have been taken by your team in a given game, predict how any goals have been scored.
e. Conduct a complete hypothesis test using the graphical and p-value method to determine if your theory regarding shooting and scoring is correct (thus proving the parents wrong). Your confidence level should be set at 95%.
Game: 1 2 3 4 5 6 7 8 9 10
Shots (x): 25 38 43 32 36 23 30 45 46 37
Goals (y): 3 5 7 5 4 0 3 4 4 3
a. Find the linear equation of regression for the line of best fit.
b. Compute the correlation coefficient (r).
c. Estimate the number of shots that would be needed in order to score 8 goals.
d. If it is known that 43 shots have been taken by your team in a given game, predict how any goals have been scored.
e. Conduct a complete hypothesis test using the graphical and p-value method to determine if your theory regarding shooting and scoring is correct (thus proving the parents wrong). Your confidence level should be set at 95%.
From a random sample of 22 cities of various sizes, data is collected from police records regarding violations of the narcotic drug laws per 100,000 inhabitants. The communities were broken down into 4 sizes (large cities, small cities, suburban communities, and rural communities), and data was collected over the period of one calendar year. Please determine if there is significant evidence to conclude that the mean rates of arrests for narcotics is different in each community (based on their size). Please conduct this test at the 99% confidence level.
City Community
Large: 45, 34, 41, 42, 37 Suburban: 25, 17, 19, 28, 31, 37
Small: 23, 24, 27, 21, 26, 34 Rural: 13, 16, 14, 17, 10
City Community
Large: 45, 34, 41, 42, 37 Suburban: 25, 17, 19, 28, 31, 37
Small: 23, 24, 27, 21, 26, 34 Rural: 13, 16, 14, 17, 10
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#339914 on Dec 2023
#339914 on Dec 2023