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Cos²x + sin2x - 1 = 0, 0° ≤ x ≤ 90°, tan x =​

Answers

Answer 1
Answer:

Answer:

0 and arctan(0.5)

Step-by-step explanation:

if sin2x=2sinx*cosx and 1=sin²x+cos²x, then

cos²x+2sinxcosx-sin²x-cos²x=0;

2sinxcosx-sin²x=0; (to divide by cos²x)

2tanx-tan²x=0;

\left[\begin{array}{ccc}tan(x)=0\n tan(x)=1/2\end{array} \ => \ \left[\begin{array}{ccc}x=pi*n\nx=arctan(1/2)+pi*n\end{array} \ => \ \left[\begin{array}{ccc}x=0\nx=arctan(0,5)\end{array}

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Kellen bought a souvenir cup at the zoo for $7.50. Any time Kellen bringsthecup back to the zoo, he can purchase fountain drinks for $0.75 each. IfKellen has spent $12.75 so far, including the original purchase of the cup,how many fountain drinks has he purchased?
WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS HELPPPPPWrite an equation parallel to x-4y=20 that passes through the point 2,-5

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.

"write a program that takes as input an arithmetic expression. the program outputs whether the expression contains matching grouping symbols. for example, the arithmetic expressions {25 + (3 – 6) * 8} and 7 + 8 * 2 contains matching grouping symbols. however, the expression 5+{(13+7)/8-2*9 does not contain matching grouping symbols."

Answers

theprogram outputs whether the expression contains matching groupingsymbols. for example, the arithmetic expressions {25 + (3 – 6) * 8} and 7+ 8 * 2 contains matching grouping symbols. however, the expression5+{(13+7)/8-2*9 does not contain matching grouping symbols.

21) Which is the correct reasoning to use when simplifying this expression?

−200 ÷ −25
A) The quotient of two even integers is always positive.
B) The product of two even integers is always positive.
C) The quotient of two negative integers is always negative.
D) The quotient of two negative integers is always positive.

Answers

D) The quotient of two negative integers is always positive. 
THe correct answer is D. ex : 9×-3= -27
-27÷-3= 9

Caroline needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 2.75 hours and charged her $114 for parts. The total was $320.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.​

Answers

2.75(x)+114=320.25
-114 -114
2.75(x)=206.25
/2.75. /2.75
X=75

It costs 75$ per hour


This is because we don’t know how much they charge per hour but we know the number of hours spend working on the computer, so you have to do 2.75(x) where x represents the cost per hour And we also know that the cost of the part is $114 so we have to add that to
(2.75(x)+114) the equation then finally you have to make the expression equal to 320.25 since we know the final cost so

2.75(x)+114=320.25

Final answer:

The equation to solve this problem is 114 + 2.75x = 320.25. Solving this equation, we find that the cost of labor per hour, represented by x, is $75.

Explanation:

The problem you're trying to solve involves the labor cost per hour of the technician who worked on Caroline's computer. From the problem, we know that the total cost of the repair was $320.25. This includes the cost of parts, which was $114, and the labor the technician invested, which we know took 2.75 hours but we aren't sure of the per hour cost. Let's denote this unknown cost as x. Therefore, our equation would be 114 + 2.75x = 320.25.

We can solve for x, the cost of labor per hour, by isolating this variable on one side of the equation. Firstly, subtract 114 from both sides: 2.75x = 320.25 - 114 which results in 2.75x = 206.25. Then, divide both sides by 2.75 to find x: x = 206.25/2.75 which equals $75. Therefore, the cost of labor per hour is $75.

Learn more about Labor Cost here:

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Please Answer the following with explanation and formula with neat typing

Answers

Answer: A

Step-by-step explanation:

You want to make them both have common denominators. What number does the denominators both go into? Thats easy, its 60.

Multiply 7/12 by 5/5 to get 35/60

Now multiply 4/15 by 4/4 to get 16/60

You need to add a negative number to 35/60 in order to get 16/60

Do 16-35 to get -19/60

Question 1Two packs of toilet rolls are available in the
supermarket 9 toilet rolls for £3.15 4 toilet rolls for £1.36
Work out which pack offers the best value for money.
​

Answers

Answer:

for the nine toilet pack, a toilet roll is 3.15/9 which is£0.35 while for the 4 toilet roll pack, a toilet roll is 1.36/4 which is £0.34 so the nine toilet pack gives the best value for money because a toilet roll sells for £0.35 which is £ 0.01 more than the four toilet pack
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