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Aleonysh [2.5K]
3 years ago
14

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

                        =0


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
Please really need help on this please
astraxan [27]

Answer:

22222.#2345/(87559grudj

4 0
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:

-440, -4440, -44440, -444440, -4444440

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

7 0
3 years ago
Which equation can be used to represent the statement?
Arte-miy333 [17]

You need to specify the statement needed to use the equation. Thank you. I will then answer it if needed.

3 0
3 years ago
What is 1/4 of 76 in a mathequ on
Softa [21]
The answer is 19. You have to do 1/4 x 76/1 which is basically 76 divided by 4, which gives you 19.
4 0
2 years ago
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