Question

in cartesian coordinates, the three corners of a triangle are P1=(0,4,4), P2=(4,-4,4), and P3=(2,2,-4)

a) find the area of the triangle

b) find the shortest distance from the origin

Answer #1

Three point of measurement coordinates are collected on a circle
(X,Y,Z): P1(14,21,8), P2(45,22,8) and P3(65,19,8) (all measurements
in mm).
Calculate the center of Y-Coordinate of the circle.

The Cartesian coordinates of a point are given. (a) (−4, 4) (i)
Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤
θ < 2π. (r, θ) (ii) Find polar coordinates (r, θ) of the point,
where r < 0 and 0 ≤ θ < 2π. (r, θ) (b) (3, 3 3 ) (i) Find
polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ
< 2π. (r, θ) =...

IN C++ - most of this is done it's just missing the bolded
part...
Write a program that creates a class hierarchy for simple
geometry.
Start with a Point class to hold x and y values of a point.
Overload the << operator to print point values, and the + and
– operators to add and subtract point coordinates (Hint: keep x and
y separate in the calculation).
Create a pure abstract base class Shape, which will form the
basis...

Three point charges are on the corners of an isosceles triangle
(a triangle where two sides have equal length). The distance
between ?1and ?2is ?and the distance between ?3and both ?1and ?2is
5?. The three charges have the relative values (?> 0):Q1=-3Q ,
Q2=2Q , Q3= 5Q
a)Draw diagrams showing the individual electric forces from the
other charges and the total electric force on each charge.
b) Solve for the x and y components of the total electric field
at...

Genotypes AA, Aa, and aa occur with probabilities (p1,p2,p3).
For n = 3 independent observa-
tions the observed frequencies are (y1, y2, y3).
(a) Explain how you can determine y3 from knowing y1 and y2.
Thus the multinomial distribution
of (y1, y2, y3) is actually two-dimensional.
(b) Show the set of all possible observations, (y1, y2, y3) with
n = 3.
(c) Suppose (p1, p2, p3) = (0.25, 0.5, 0.25). Find the the
probability that (y1, y2, y3) = (1,...

Using definite integrals, find the area of the triangle formed
by the given (x, y) coordinates. Do the problem by hand. Give your
final answer rounded to three decimals using your calculator. (0,0)
, (2, 5) , (4, 1)

Three 6.8 micro coulomb charges are arranged at the corners of a
an equilateral triangle with sides of length 0.3 meters. They are
held in place initially. The charges have a mass of 10 grams. One
side of the triangle is on the horizontal axis.
Find :
a) size of the force, in Newtons, acting on the charge at the
top of the triangle due to the other two charges
b) the direction of the force, in degrees, as measured...

Three 5.8 micro coulomb charges are arranged at the corners of a
an equilateral triangle with sides of length 0.6 meters. They are
held in place initially. The charges have a mass of 10 grams. One
side of the triangle is on the horizontal axis.
Find the:
a) size of the force, in Newtons, acting on the charge at the
top of the triangle due to the other two charges,
b) the direction of the force, in degrees, as measured...

let p1(x) = x^2-3x-10 ,p2(x)=x^2-5x+1,p3(x)=x^2+2x+3 and
p4(x)=x+5
a- As an alternative ; we can form additional equation involving
a1,a2,a3,and a4 using differntiation.explain how how to produce a
system of equation with unknown constant a1,a2,a3,a4. Since there
are 4 unknown ,you will need 4 equattion find them
b- Find Basis for the vector space spanned by
p1(X),p2(x),p3(x),p4(x). express any reductant vector in terms of
linear combination of the others .Note you might want to use row in
the changes?

Let P1 = number of Product 1 to be produced
P2 = number of Product 2 to be produced
P3 = number of Product 3 to be produced
P4 = number of Product 4 to be produced
Maximize 15P1 + 20P2 + 24P3 + 15P4 Total profit
Subject to
8P1 + 12P2 + 10P3 + 8P4 ≤ 3000 Material requirement
constraint
4P1 + 3P2 + 2P3 + 3P4 ≤ 1000 Labor hours constraint
P2 > 120 Minimum quantity needed for...

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