All categories

3 years ago

Which of the following equations is quadratic?

Mathematics

2 answers:

Sindrei [870]3 years ago

7 0

Answer:

I think it's 2 because the quadratic equation looks like this ax^2+bx+c=0 and option 2 looks like it.

Step-by-step explanation:

For option 1: x(x^2+1)=0

x^3+1=0 ( This also does not look like the quadratic function, so it couldn't be the answer)

For option 2: (x+3)(x+4)=5

x^2+3x+3x+12=5

x^2+6x+12=5 ( This does look like the quadratic function, so it could be the answer)

For option 3:

5(4x+2)=3

20x+10=3 ( This also does not look like the quadratic function, so it couldn't be the answer)

snow_lady [41]3 years ago

3 0

Answer:

the first one

x(x2 + 1)= 0

You might be interested in

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0

3 years ago

Don wants to keep his favorite pine tree from being uprooted by heavy winds. He plans to tie 3 sections of rope to a band on the

iragen [17]

Answer:64 feet i think

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Finish your work.<br> Do it for him

VMariaS [17]

Answer:

LOL WHATS DIS HUNNNYYY

Step-by-step explanation:

8 0

3 years ago

What is 25x3.08?? Help me plz

charle [14.2K]

It is 7 .....................................................

7 0

3 years ago

Read 2 more answers

If y =<br> ya<br> x and x = -18, find y.

vampirchik [111]

Answer:

√

−

√

−

Step-by-step explanation:

4 0

3 years ago