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Bad White [126]
2 years ago
9

A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days). Assume that the number o

f hours of daylight varies sinusoidal over a period of twelve months. Sketch the graph then use this data to find the following:
Mathematics
1 answer:
OLga [1]2 years ago
8 0

We have that the graph will have a solution that is mathematically given as

y=12sin(6t-\pi)+2

<h3>Daylight time June trough to December</h3>

Question Parameters:

A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days).

Generally the equation for the Amplitude and vertical shift is mathematically given as

A=\frac{Max+min}{2}\\\\A=\frac{10+14}{2}

A=2

vertical shift =\frac{Max-min}{2}

vertical shift =\frac{14-10}{2}

vertical shift =1

Therefore, the time is given as

t=\frac{2\pi}{b}

Where

b=\pi/6\\\\t=\frac{2\pi}{\pi/6}

Hence,The graph will have a solution

y=12sin(6t-\pi)+2

For more information on Graph

brainly.com/question/14375099

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pentagon [3]
Answer: 35%

1. 26 fiction books divided by all 40 books equals 65% fiction books.

2. Then do 100% - 65% to get 35%

OR

1. All 40 books minus 26 fiction books
= 14 nonfiction books.

2. Do 14 divided by 40 to get 0.35, = 35%
4 0
3 years ago
The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesse
yuradex [85]

Answer:


Step-by-step explanation:

Let x be the greater number and y be the smaller number. We know that their difference is 15, so we have

x-y=15

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have

2x+8 = 3y-4 \iff 2x-3y = -12

So, we have the follwing system:

\begin{cases} x-y=15\\2x-3y = -12\end{cases}

From the first equation, we can derive x = y+15, and substitute this expression in the second equation to get

2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42

Substitute this value for y in the first equation to get

x-42=15 \iff x=15+42 \iff x = 57

8 0
3 years ago
Monty documented the amount of rain his farm received on a monthly basis, as shown in the table.
hammer [34]

Answer:

No

Step-by-step explanation:

Because we need to see the table and information provided on the table otherwise we can't help you solve your problem.

5 0
3 years ago
find the spectral radius of A. Is this a convergent matrix? Justify your answer. Find the limit x=lim x^(k) of vector iteration
Natasha_Volkova [10]

Answer:

The solution to this question can be defined as follows:

Step-by-step explanation:

Please find the complete question in the attached file.

A = \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right]

now for given values:

\left[\begin{array}{ccc} \frac{3}{4} - \lambda & \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2} - \lambda & 0\\ -\frac{1}{4}& -\frac{1}{4} & 0 -\lambda \end{array}\right]=0 \\\\

\to  (\frac{3}{4} - \lambda ) [-\lambda (\frac{1}{2} - \lambda ) -0] - 0 - \frac{1}{4}[0- \frac{1}{2} (\frac{1}{2} - \lambda )] =0 \\\\\to  (\frac{3}{4} - \lambda ) [(\frac{\lambda}{2} + \lambda^2 )] - \frac{1}{4}[\frac{\lambda}{2} -  \frac{1}{4}] =0 \\\\\to  (\frac{3}{8}\lambda + \frac{3}{4} \lambda^2 - \frac{\lambda^2}{2} - \lambda^3 - \frac{\lambda}{8} + \frac{1}{16}=0 \\\\\to (\lambda - \frac{1}{2}) (\lambda -\frac{1}{4}) (\lambda - \frac{1}{2}) =0\\\\

\to \lambda_1=\lambda_2 =\frac{1}{2}\\\\\to \lambda_3 = \frac{1}{4} \\\\\to A = max {|\lambda_1| , |\lambda_2|, |\lambda_3|}\\\\

       = max{\frac{1}{2}, \frac{1}{2}, \frac{1}{4}}\\\\= \frac{1}{2}\\\\(A) =\frac{1}{2}

In point b:

Its  

spectral radius is less than 1 hence matrix is convergent.

In point c:

\to c^{(k+1)} = A x^{k}+C \\\\\to x(0) =   \left(\begin{array}{c}3&1&2\end{array}\right)  , c = \left(\begin{array}{c}2&2&4\end{array}\right)\\\\  \to x^{(k+1)} =  \left[\begin{array}{ccc} \frac{3}{4}& \frac{1}{4}& \frac{1}{2}\\ 0 & \frac{1}{2}& 0\\ -\frac{1}{4}& -\frac{1}{4} & 0\end{array}\right] x^k + \left[\begin{array}{c}2&2&4\end{array}\right]  \\\\

after solving the value the answer is

:

\lim_{k \to \infty} x^k=o  = \left[\begin{array}{c}0&0&0\end{array}\right]

4 0
3 years ago
Two more than a certain number is 15 less than the product of 7/8 and the number
valkas [14]
Whats your question bro? whats the number? the number is
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3 years ago
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