The roots routine will return a column vector containing the roots of a polynomial. The general syntax is
z = roots(p)
where p is a vector containing the coefficients of the polynomial ordered in descending powers.
Given a vector
which describes a polynomial
we construct the companion matrix (which has a characteristic polynomial matching the polynomial described by p), and then find the eigenvalues of it (which are the roots of its characteristic polynomial)
Example
Here is an example of finding the roots to the polynomial
--> roots([1 -6 -72 -27])
ans =
12.1229
-5.7345
-0.3884
The rectangle problem:
First, create some variables.
w = width
l = length
Then you know that the length is 3 times the width, so
l = 3w
The equation for perimeter is
P = 2(l+w)
Now you use substitution, substituting the 3w for l because you found that earlier.
P = 2((3w) + w)
And simplify.
P = 2(4w)
P = 8w
And you know P = 30 because they told you that.
30 = 8w
w = 15/4 inches, or 3.75 inches
Now substitute that value back into that first equation,
l = 3w
l = 3(15/4)
l = 45/4 inches, or 11.25 inches.
The dimensions are 11.25in for length and 3.75in for width.
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The volleyball problem:
100 minutes of stretching and scrimmaging combined, and you know 10 have to be stretching, so 90 is scrimmaging.
s = scrimmaging
T = total time
s = 2/3T (they gave you this)
90 = 2/3T
T = (90*3)/2
T = 270/2
T = 135 minutes, or 2 hours and 15 minutes.
Let the shorter leg = a.
The longer leg, b = a + 4.
The hypotenuse, c = a + 8
a^2 + b^2 = c^2
a^2 + (a + 4)^2 = (a + 8)^2
a^2 + a^2 + 8a + 16 = a^2 + 16a + 64
a^2 - 8a - 48 = 0
(a - 12)(a + 4) = 0
a - 12 = 0 or a + 4 = 0
a = 12 or a = -4
a = -4 is discarded because it is negative.
a = 12
b = 16
c = 20
The lengths are 12 m, 16 m, and 20 m.
Answer:
x = 24
Step-by-step explanation:
Since all the angles share a common vertex 'U' lying on a straight line QT.
Therefore, sum of all angles formed at U will be equal to 180°.
m∠RUQ + m∠RUS + m∠SUT = 180°
(2x - 4) + (3x + 5) + (2x + 11) = 180°
(2x + 3x + 2x) + (5 - 4 + 11) = 180
7x + 12 = 180
7x = 180 - 12
x = 
x = 24
Therefore, value of x = 24
Answer:
11 1/9 - 3 2/3 = 7 3/9
Step-by-step explanation:
First you have to turn 2/3 into ninths which would be 6/9. Then you have to turn 1/9 into 10/9 by giving one whole and turning it into a fraction. Then you have to subtract 10/9 - 6/9 = 3/9. Finally you have to subtract the wholes 10-3= 7 then your answer would be 7 3/9
