Question

1. Use the x- and y- intercepts to graph each linear equation.(Do not use graph paper)

a) 2x-5y=10

b) 3x=2y+6

2. Calculate the slope of the line passing through the given points. If the slope is undefined, so state, Then indicate whether the line rises, falls, is horizontal or is vertical.

a) (4,2) and (3,4)

b) (-1,3) and (2,4)

Answer #1

Consider the function f(x) = √x and
the point P(4,2) on the graph f.
a)Graph f and the secant lines passing through the
point P(4, 2) and Q(x,
f(x)) for x-values of 3, 5, and 8.
b) Find the slope of each secant line. (Round your answers to
three decimal places.)
(line passing through Q(3, f(x)))
(line passing through Q(5, f(x)))
(line passing through Q(8, f(x)))
c)Use the results of part (b) to estimate the slope of the
tangent line...

17.
Match the information about each graph with the correct linear
equation.
Information
Linear Equations
(a)
The graph of the equation has
y-intercept
(0,−99).
A.
6 x plus y equals negative 96x+y=−9
(b)
The graph of the equation has (0, 0) as x-intercept and
y-intercept.
B.
y equals 4 xy=4x
(c)
The graph of the equation does not have an x-intercept.
C.
y equals 7y=7
(d)
The graph of the equation has
x-intercept
(77,0).
D.
x minus 7 equals 0...

Use Gauss-Jordan method (augmented matrix method) to
solve the following systems of linear equations. Indicate whether
the system has a unique solution, infinitely many solutions, or no
solution. Clearly write the row operations you use. (a) (5 points)
x + y + z = 6 2x − y − z = 3 x + 2y + 2z = 0 (b) (5 points) x − 2y
+ z = 4 3x − 5y + 3z = 13 3y − 3z =...

The following constraints of a linear programming model have
been graphed on the graph paper provided (same constraints found in
problem #3) to form a feasible region:
2X + 6Y
>= 120
10X + 2Y > = 200
X +
Y <= 120
X
<= 100
Y <= 80
X,Y
>= 0
Using the graphical method, determine the optional solution and
the objective function value for the following objective functions.
Graph the objective function as a dashed line on...

1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) =
(2y − z, x − z, y + 3x). Use matrices to find the composition S ◦
T.
2. Find an equation of the tangent plane to the graph of x 2 − y
2 − 3z 2 = 5 at (6, 2, 3).
3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...

Find an equation for each of the following planes. Use x, y and
z as the variables.
a) An equation of the plane passing through the points (1,−1,1),
(0,−2,−1) and (−4,0,6)
b) An equation of the plane consisting of all points that are
equidistant (equally far) from (−3,−5,−1) and (4,−1,−3)
c) An equation of the plane containing the line
x(t)= [0, -1, 1] + t[0, 4, -1] and is
perpendicular to the plane 3y − 4z = −7

1. (a) Use the graph paper provided to sketch the region bounded
by the x-axis and the lines x + y = 4 and y = 3x.
(b) Shade the region you just drew above.
(c) Suppose that you were going to use Calculus to compute the
area of the shaded region in part (a) above. If you chose the
x-axis as your axis of integration, then how many integrals would
be needed to compute this area?
(d) Suppose that...

1. Let f(x)=(x^2+1)(2x-3)
Find the equation of the line tangent to the graph of f(x) at
x=3.
Find the value(s) of x where the tangent line is horizontal.
2. The total sales S of a video game t months after being
introduced is given by the function
S(t)=(5e^x)/(2+e^x )
Find S(10) and S'(10). What do these values represent in terms
of sales?
Use these results to estimate the total sales at t=11 months
after the games release.

A statistical program is recommended.
Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized...

Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized residual with the largest absolute...

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