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Ad libitum [116K]
3 years ago
5

An expression to convert 50 miles per hour to miles per minute is shown.

Mathematics
1 answer:
aev [14]3 years ago
6 0

Answer:

(50 mi/h) (1 h/60 min)

Step-by-step explanation:

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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}

3 0
1 year ago
Mr. Sanchez’s class sold fruit pies for $1.73 each and Mr. Kelly’s class sold bottles of fruit juice for $1.44 each. Together, t
-Dominant- [34]

Answer:

p = 39       f = 44    

Step-by-step explanation:

p = $ 1.73

f = $ 1.44

<u><em>equation </em></u>

p + f = 83

1.73 p + 1.44 (83 - p) = $ 130.83

p = 39 (amount of times fruit pies were sold).

Therefore,

<em>p = 39</em>

<em>f = 44</em>

4 0
1 year ago
What is the whole number 11 minus the number 3 4/12 show your work
olga2289 [7]

1.) 11 - 3 4/12

2.) 11 - 3 1/3    

3.) 11/1  - 3 1/3

4.) 33/3 -  10/3  

5.) 23/3 or 7.7 or 7 2/3 is your answer, depending on how you want it

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3 years ago
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VARVARA [1.3K]

\huge{\boxed{26.98}}

The hundredths place is the second place after the decimal point. In this case, it is 8.

We can round it by looking at the next place to the right, which is a 1. 1 is less than 5, so we can just cut off everything after the hundredths place. This leaves an answer of \boxed{26.98}.

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99% were not broken as only 1% were broken
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