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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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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.

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The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E

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Total displacement

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Angle with east direction

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Ф = 15 degree  south of east.

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3 years ago
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