A number cube is rolled 450 times and the

I REALLY NEED HELP PLEASE

Ira Lisetskai [31]

I think the answer is letter B

6 0

3 years ago

Given the following roots build a polynomial function in standard form: -3 and +2

swat32

Answer:

f(x) = x² +x -6

Step-by-step explanation:

The standard form will look like ...

f(x) = x² +bx +c

where b is the opposite of the sum of the roots, and c is their product.

f(x) = x² -(-3+2)x +(-3)(2)

f(x) = x² +x -6

_____

Additional comment

In general, "standard form" is ax²+bx+c. In this case, the coefficient 'a' can be 1 since neither of the roots is expressed as a fraction. The sum of roots is (-b/a) and the product of roots is (c/a).

3 0

3 years ago

Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

Mashcka [7]

The cone equation gives

$z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2$

which means that the intersection of the cone and sphere occurs at

$x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92$

i.e. along the vertical cylinder of radius $\dfrac3{\sqrt2}$ when $z=\dfrac3{\sqrt2}$ .

We can parameterize the spherical cap in spherical coordinates by

$\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle$

where $0\le\theta\le2\pi$ and $0\le\varphi\le\dfrac\pi4$ , which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is $\dfrac3{\sqrt2}$ . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

$\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4$

Now the surface area of the cap is given by the surface integral,

$\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du$
$=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}$
$=18\pi\left(1-\dfrac1{\sqrt2}\right)$
$=9(2-\sqrt2)\pi$

3 0

3 years ago

Fill in the missing fraction or mixed number __ + 1/4 = 5/8

gogolik [260]

3/8=answer

1) 5/8-1/4=

2) (5•4)-(1•8)=

8•4

3) 20-8

32 =

4) 12

32=

5) 12/4

32/4=

6) 3

8 =answer

5 0

3 years ago

Solve x 2 + 8x + 7 = 0 {-1,-7) {1,7) 00

IgorLugansk [536]

X^2 + 8x + 7= 0
(X+7)(X+1)
X=-1,-7

3 0

3 years ago