In: Advanced Math

Express the equation of the plane in explicit form

a. d = [1, -3, -5]; e = [-2, 1, -1] and f = [5, -1, -3] Express the
equation of the plane through d, e, and f explicitly

b. d = [-1, 7, -6]; e = [2, -1, 3] and f = [4, -2, 9] Express the
equation of the plane through d, e, and f explicitly

Dear student,

When ever we want to find the explicit equation of the plane passing through three points,first we find the normal vector to the plane.I have explicitly stated the explanation, procedure,and formula to calculate the equation of plane in the below image.

A group of 100 students form 5 voting blocs, A, B, C, D, and E.
They agree to use 57 votes as the number needed to pass a motion.
This results in the following voting structure:
[57 : 34,28,20,14,4]
Identify the number of voting blocs that have zero voting power as
measured by the Banzhaf Power Index.
a)0 voting blocs
b)Exactly 1 voting bloc
c)Exactly 2 voting blocs
d)Exactly 3 voting blocs
e)Exactly 4 voting blocs
f)Exactly 5 voting blocs

1. Consider the spiral S in the xy-plane given in polar form by
r = e ^θ . (a) (5 points) Find an arc length parametrization for S
for which the reference point corresponds to θ = 0.
(b) (5 points) Compute the curvature of S at the point where θ =
π.

Find an equation of the tangent plane to g(x,y)=e^(4x) -2xy+y^3
at (0,1)

1. Express the following complex numbers in cartesian form x +
jy: 1/2 e jπ , 1/2 e −jπ , √ 2e j9π/4 , √ 2e −j9π/4
2. Express the following complex numbers in polar form rejθ with
−π < θ ≤ π: 5, −2, 1/2 − j √ 3/2, (1 + j)/(1 − j).
PLEASE ANSWER WITH FULL STEPS AND CORRECT.

1.Express the confidence interval (45.3%,61.9%) in the form of
ˆp ± E
2.Assume that a sample is used to estimate a population
proportion p. Find the 80% confidence interval for a
sample of size 260 with 24% successes. Enter your answer as a
tri-linear inequality using decimals (not percents) accurate to
three decimal places.
3.Out of 400 people sampled, 240 preferred Candidate A. Based on
this, estimate what proportion of the entire voting population (p)
prefers Candidate A.
Use a...

1. Processes A, B, C, D, E, and F require service times of 3, 5,
2, 5, 3, and 5. Their arrival times are 0, 1, 3, 9, 10, and 12.
What is the average turnaround time, waiting time, response time,
and throughput when using SRJF, RR (q=2), and MLF
(q=22i+1). Show your work.

1. Processes A, B, C, D, E, and F require service times of 3, 5,
2, 5, 3, and 5. Their arrival times are 0, 1, 3, 9, 10, and 12.
What is the average turnaround time, waiting time, response time,
and throughput when using SRJF, RR (q=2), and MLF
(q=22i+1). Show your work.

A maximal plane graph is a plane graph G = (V, E) with n ≥ 3
vertices such that if we join any two non-adjacent vertices in G,
we obtain a non-plane graph.
a) Draw a maximal plane graphs on six vertices.
b) Show that a maximal plane graph on n points has 3n − 6 edges
and 2n − 4 faces.
c) A triangulation of an n-gon is a plane graph whose infinite
face boundary is a convex n-gon...

Find an equation of the plane that passes through the point (1,
7, 3) and cuts off the smallest volume in the first octant.

f(x) = -3x2+16x-5
e) Find (in y=mx+b form) the equation of the line that contains
the vertex and the largest of the x-axis intercepts. If there are
decimals round to the tenths place.
f) Find the length of the line segment that is between the
vertex and the largest of the x-axis intercepts.

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