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3 years ago

Help please if you still up im really struggling

Mathematics

1 answer:

Papessa [141]3 years ago

3 0

Answer:

discriminant =0

1 real root

Step-by-step explanation:

The discriminant is b^2 -4ac

when the equation is written in the form ax^2 +bx+c

f(x) = 3x^2 +24x+48

a = 3 b = 24 and c =48

discriminant = 24^2 - 4(3)*(48)

=576-576

If the discriminant >0 we have 2 real roots

if discriminant = 0 we have 1 real root

if discriminant <0 we have 2 complex roots

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Convert the integral below to polar coordinates and evaluate the integral.

Lelechka [254]

Answer:

$\int\limits_{0}^{4/\sqrt{2}}\int\limits_{y}^{\sqrt{16-y^2}} xy \, dxdy = \int\limits_{0}^{\pi/4} \, \int\limits_{0}^{4} r^3 cos(\theta)\sin(\theta) \,\, drd\theta = 16$

Step-by-step explanation:

We are trying to evaluate this integral.

$\int\limits_{0}^{4/\sqrt{2}}\,\,\int\limits_{y}^{\sqrt{16-y^2}} xy \,\,dxdy$

The first thing that we have to do is understand this region in the plane.

$\{ (x,y) \in \mathbb{R} : 0\leq y \leq \frac{4}{\sqrt{2}} \,\, , y \leq x \leq \, \sqrt{16-y^2} \}$

If you graph it looks something like the photo I join.

Now we need to describe that same region in polar coordinates.

That same region in polar coordinates would be

$\{ (r,\theta) : \,\, 0 \leq \theta \leq \frac{\pi}{4} \,\,\, 0\leq r \leq 4 \}$

Now remember that when we do the polar transformation we use the following formula

$\int\limits_{a}^{b} \, \int\limits_{c}^{d} f(x,y) \,dxdy = \int\limits_{\theta_1}^{\theta_2} \, \int\limits_{r_1}^{r_2} r* f(rcos(\theta),rsin(\theta)) \,drd\theta$

Then our integral would be

$\int\limits_{0}^{4/\sqrt{2}}\int\limits_{y}^{\sqrt{16-y^2}} xy \, dxdy = \int\limits_{0}^{\pi/4} \, \int\limits_{0}^{4} r^3 cos(\theta)\sin(\theta) \,\, drd\theta = 16$

6 0

3 years ago

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astraxan [27]

Answer:

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2 years ago

find five solutions of the equation y=20x. select integers for values for x starting with -2 and ending with 2

Nataly_w [17]

Answer:

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Step-by-step explanation:

First, let's find values for x which start is a -2 and end with a 2.

-22

-222

-2222

-22222

-222222

Now we can find the y value by multiplying each term by 20.

-22 --> -440

-222 --> -4440

-2222 --> -44440

-22222 --> -444440

-222222 --> -4444440

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