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kobusy [5.1K]
2 years ago
13

1,729 is divisible by 9 a. true b. false

Mathematics
1 answer:
alexgriva [62]2 years ago
3 0
It is b: False 1,729 isn’t divisible by 9
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Y varies directly with x, and y = 15 when x = 3. What is the value of x when y = 4?
TiliK225 [7]
When x = 3 , y = 15 , divide both by 3.
When x= 1 , y = 5. Now multiply both by 4/5
When x = 4/5 , y=4
8 0
3 years ago
Read 2 more answers
√-225 • √-36 . show work.
Darya [45]

Answer:

±90

Step-by-step explanation:

√(-225) · √(-36) = (15i)·(6i) = 90i² = 90·(-1) = -90

_____

On the other hand, ...

... √(-225) · √(-36) = √((-225)·(-36)) = √8100 = 90

___

If you consider all the roots at each stage, the result is ±90. Since you're working with complex numbers here, it is reasonable to recognize every number has two square roots.

... √(-225) = ±15i

... √(-36) = ±6i

... √(-225) · √(-36) = (±15i)·(±6i) = ±90i² = ±90

7 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
The volume of a pyramid with a square base where the area of the base is 8.7m^2 and the height is 10
MrMuchimi

Answer:

  29 m³

Step-by-step explanation:

The applicable formula is ...

  V = (1/3)Bh

Assuming the height is 10 m, the volume is ...

  V = (1/3)(8.7 m²)(10 m) = 29 m³

_____

The shape of the base is irrelevant.

5 0
3 years ago
A rectangular solid with a square base has a volume of 8000 cubic inches. determine the dimensions that yield
stiks02 [169]
A rectangular solid with a square base has a volume of 8000 cubic inches<span>.</span>
6 0
3 years ago
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