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4 years ago

Find the vertex of the graph of the function. f(x) = 2x2 - 8x + 9

Mathematics

1 answer:

Katen [24]4 years ago

8 0

Answer:

(2, 1).

Step-by-step explanation:

f(x)=2x^2-8x+9

Find -b/2a first, it's -(-8)/2(2)=8/4=2.

Then find the y-coordinate of the vertex.

2(2)^2-8(2)+9=2(4)-16+9=8-16+9=-8+9=1

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MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

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saw5 [17]

Answer:

Step-by-step explanation:

Hello,

First of all we will take any real number x different from 0, -2, +2 as dividing by 0 is not allowed and then we can write

$\dfrac{( - x - 2)}{x(x^2 - 4)}=-\dfrac{x+2}{x(x-2)(x+2)}=\large \boxed{ -\dfrac{1}{x(x-2)}}$

because we know that

$x^2-4=x^2-2^2=(x-2)(x+2)$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

8 0

3 years ago

Donna made $396 for 18 hours of work.

amm1812

Answer:

$286

Step-by-step explanation:

396/18 = $22 per hr x 13 hrs = $286

Plz give Brainliest

5 0

3 years ago

write a linear equation in slope-intercept form with a slope of -5 and passes through the point (-1,8)

hammer [34]

Answer:

y=-5x-13

Step-by-step explanation:

use y-y1=m(x-x1)

y+8=-5(x+1)

y+8=-5x-5

subtract 8 from both sides

y=-5x-13

8 0

3 years ago

PLEASE HELP LOTS OF POINTS

Cloud [144]

Answer:

Yes

Step-by-step explanation:

they are on the same plane

5 0

3 years ago

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