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Ludmilka [50]
3 years ago
11

The directex of Y=1/8x^2 is?

Mathematics
1 answer:
nexus9112 [7]3 years ago
6 0
\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
y=\cfrac{1}{8}x^2\implies (y-0)=\cfrac{1}{8}(x-0)^2\implies 8(y-0)=(x-0)^2
\\\\\\
4(2)(y-0)=(x-0)^2\impliedby \textit{that means, p = 2}

so... if you notice, the vertex is at h,k and that'd be the origin, 0,0

so...since the directrix is "p" units from the vertex, so it'd be 2 units from 0,0

now, the parabola has an equation with a positive leading term's coefficient, namely the 1/8 is positive, thus, the parabola is opening upwards, and the directrix is "outside" the parabola, so is below the vertex

that puts the directrix 2 units below 0,0

y = -2
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Evaluate: [(21 + 6) − 32] ÷ 9.2 A) 4. B) 4.6. C) 1. D) 52.
Dima020 [189]
[(21 + 6) - 32] : 9.2 = (27 - 32) : 9.2 = -5 : 9.2 = -46
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3 years ago
6 apple trees fir every 4 pears trees How many apple trees would there be if there were 42 pear trees
SIZIF [17.4K]
Answer: 63 apple trees
Explanation: divide 42 by 4 to get that amount of groups (10.5) then multiply that number by 6 so (10.5 • 6) and that should give the apple tree total.
4 0
3 years ago
Help please... I'm close to be done soon... of my little sister homework...
harkovskaia [24]

C' = (6,-1) or (-1,6)

D'= (6,6)

E'= (-4,1) or (1,-4)

Hope this helps somewhat

5 0
2 years ago
Read 2 more answers
The boy wants to build rectangular beetle cages to study beetle behavior. He wants all the sides on the base of his cages to be
kap26 [50]

Answer:

32 cm by 18 cm

16 cm by 36 cm,

48 cm by 12 cm

24 cm by 24 cm

Step-by-step explanation:

<u><em>The complete question is</em></u>

A boy wants to build rectangular cages. He wants all the sides on the base of his cages to beat least 10 cm long.he also wants the base area to equal 576 cm2. The boy needs help to find all the possible lengths and widths for the base of the cages. He used only whole centimeters, with no fractional parts.what are all the possible dimensions for the rectangular base?

we know that

The number 576 decompose in prime factors is the same that write

576=(2^6)(3^2)

To find out possible side lengths, multiply different combinations of these prime numbers together (make sure each pair adds up to 10)

3x3=9cm                  2x2x2x2x2x2= 64cm  ----> is not a combination (one side is not greater than 10)

3x3x2= 18cm            2x2x2x2x2= 32cm

3x3x2x2= 36cm        2x2x2x2= 16cm

3x2x2= 12cm             3x2x2x2x2= 48cm

3x2x2x2= 24cm         3x2x2x2= 24cm

therefore

32 cm by 18 cm

16 cm by 36 cm,

48 cm by 12 cm

24 cm by 24 cm

3 0
3 years ago
Calculus(Derivatives):
Zigmanuir [339]
f(x)=x^3+x^2-5x-2
\implies f'(x)=3x^2+2x-5=(3x+5)(x-1)

Critical points occur when f'(x)=0, which happens for x=-\dfrac53 and x=1.

Check the sign of the second derivative at each critical point to determine the function's concavity at that point. If it's concave (f''(x)), then a maximum occurs; if it's convex (f''(x)>0), then a minimum occurs.

You have

f''(x)=6x+2

and so

f''\left(-\dfrac53\right)=-8
f''(1)=8>0\implies f(x)\text{ is convex at }x=1

This means a maximum of f\left(-\dfrac53\right)=\dfrac{121}{27} and a minimum of f(1)=-5.
4 0
3 years ago
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