MATHEMATICS COLLEGE

A television is 28.5 inches wide and 16 inches long.Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?

Answers

Answer 1

Answer:

Answer:

33 in

Step-by-step explanation:

The Pythagorean theorem tells you ...

diagonal² = length² +width²

diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²

diagonal = √(1068.25 in²) ≈ 32.684 in

The diagonal of the television is about 33 inches.

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Enter the sum of numbers as a product of their GCF. 45 + 30

Answers

45 + 30 = 15(3 + 2) = 15(5) = 75

Convert 0.0555 m to mm

Answers

Answer:

0.0555 meter =

55.5 millimeters

Answer:

55.5mm

Step-by-step explanation:

Lines m and n are parallel. The equation of line m is y=3x+3. What is the equation of line n?

Answers

The equation for line n is y = 3x + c

What is the equation of a straight line ?

An equation of a straight line is given by y = mx+c, where m is the slope and c is the intercept on the y axis.

In the question it is given that

Lines m and n are parallel to each other.

The equation of line m is y=3x+3

The equation of line n =?

The parallel lines m an n will have same slope but different intercept.

So the slope in the line equation y=3x+3 is 3

m = 3

Taking c as the intercept by the line n on y axis.

The equation for line n is y = 3x + c

To know more about equation of a straight line

brainly.com/question/959487

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Answer:

y=3x-1

Step-by-step explanation:

You would have to change the y-intercept but that's all. Also, I put this answer into my ttm and got it right.

For the characteristic polynomialp(s) =s5+ 2s4+ 24s3+ 48s2−25s−50(a) Use the Routh-Hurwitz Criterion to determine the number of roots ofp(s) in the right-half plane, in the left-half plane, and on thejω-axis.(b) Use Matlab to determine the roots ofp(s), and verify your results in part 2a.

Answers

Answer:

1 root in the right half-plane
1 conjugate pair on the imaginary axis
2 roots in the left half-plane

Step-by-step explanation:

Without using the Routh-Hurwitz criterion at all, you know there is one positive real root. Descartes' rule of signs tells you the number of positive real roots is equal to the number of sign changes in the coefficients (perhaps less a multiple of 2). There is one sign change in + + + + - - , so there is one positive real root.

_____

(a) The Routh array starts as two rows of the polynomial's coefficients, alternate coefficients on each row. For this odd-degree polynomial, the number of coefficients is even, so no zero-padding is necessary at the right end of the second row. That is, we start with ...

$\begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\end{array}$

The next row is formed from combinations of coefficients in the two rows above. The computation is similar to that of a determinant. By matching the numbers to those in the array, you can see the pattern of the computation.

The next row values are ...

$\begin{array}{ccc}s^3&((2)(24)-(1)(48))/(2)&((2)(-25)-(1)(-50))/(2)\end{array}$

Simplifying, we find this row to be ...

$\begin{array}{ccc}s^3&0&0\end{array}$

The zero row is a special case that requires we proceed as follows. The row above (identified with s⁴) represents an "auxiliary polynomial":

$2s^4 +48s^2 -50$

To continue the process, we replace the zero row by the coefficients of the derivative of this auxiliary polynomial. Proceeding as before, the array now becomes ...

$\begin{array}{cccc}s^5&1&24&-25\ns^4&2&48&-50\ns^3&8&96\ns^2&24&-50\ns^1&112(2)/(3)&0\ns^0&-50\end{array}$

The number of sign changes in the first column (1) tells the number of roots in the right half-plane. The auxiliary polynomial will give us the remaining two pairs of roots:

$2s^4+48s^2-50=0\n\n2(s^2+25)(s^2-1)=0\n\ns=\pm 5i,\ s=\pm 1$

So, we have determined there to be ...

1 root in the right half-plane
2 roots on the jω axis
2 roots in the left half-plane

(b) The original polynomial can be factored as ...

p(s) = (s +2)(s² +25)(s +1)(s -1)

p(s) = (s +2)(s +1)(s -5i)(s +5i)(s -1)

This verifies our result from part (a).

_____

Additional comments

Any row can be multiplied by a convenient factor to simplify the arithmetic. Here, it would be convenient to divide the second row by 2 and the third row by 8.

A zero element (not row) in the first column is replaced by "epsilon" (a small positive number) and the rest of the arithmetic is continued as normal. That row is not counted (it is ignored) when counting sign changes in the first column.

Calculate the perimeter of a rectangle with a length of 17.5 cm and a width of 40 mm in cm