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NISA [10]
2 years ago
13

What is the focus of the parabola? 

xFormula1" title="y= \frac{1}{4} x^{2} -x+3" alt="y= \frac{1}{4} x^{2} -x+3" align="absmiddle" class="latex-formula">
Enter your answer in the boxes.


(__ , __)
Mathematics
2 answers:
Artemon [7]2 years ago
6 0
I just took the test, the answer is actually (-2, 3)
OlgaM077 [116]2 years ago
3 0
We know that
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
 the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2

y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3

the coordinates of the focus are (2,3)
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mihalych1998 [28]
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8 0
2 years ago
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A building is 5 feet tall. the base of the ladder is 8 feet from the building. how tall must a ladder be to reach the top of the
iris [78.8K]

The ladder must be 9.4 ft to reach the top of the building

Here, we want to get the length of the ladder that will reach the top of the building

Firstly, we need a diagrammatic representation

We have this as;

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We simply will make use of Pythagoras' theorem which states that the square of the hypotenuse is equal to the sum of the squares of the two other sides

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\begin{gathered} x^2=5^2+8^2 \\ x^2=\text{ 25 + 64} \\ x^2\text{ = 89} \\ x=\text{ }\sqrt[]{89} \\ x\text{ = 9.4 ft} \end{gathered}

5 0
1 year ago
Can someone answer 15b
NISA [10]
A)

well, we know the elevator's rate is -20 f/s, ok, so every second, is dropping 20 feet, therefore, "y" is "distance from the ground floor", so when y = 0, meaning the distance to the ground floor is 0, so you ARE at the ground floor then.

and "x" is how many seconds you've been in the elevator.

now, she got in the elevator for 6 seconds, so, the elevator went down by 20 * 6, or 120 feet down, reason why the slope is negative, when she stopped, she was 350 feet away from the ground floor still though.

if the elevator went down 120 feet, and she's still 350 feet from the ground floor, that means  she boarded the elevator at 120 + 350 feet, or 470 feet.

b)

\bf \begin{array}{lcccllll}
&\stackrel{\textit{elapsed seconds}}{x_1}&\stackrel{\textit{ft from ground-floor}}{y_1}\\
%   (a,b)
&({{ 6}}\quad ,&{{ 350}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies -20
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-350=-20(x-6)
\\\\\\
y-350=-20x+120\implies  y=-20x+\stackrel{y-intercept}{470}
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What percent of a circle is 3/6 of a circle
Vlad1618 [11]
50%
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Of the choices listed, the one attached is the rational function.

8 0
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