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3 years ago

What is the vertex of the absolute value function defined by f(x)=|x+2|+4?

Mathematics

2 answers:

prohojiy [21]3 years ago

6 0

The answer is A.) (-2,4)

Readme [11.4K]3 years ago

3 0

There is no maximum value for the term inside the absolute value signs, but there is an absolute minimum, being zero when x=-2. And when x=-2, y=4, and that is your vertex:

(-2, 4)

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Please help ik it’s a lottt but I’m really confused!

Juli2301 [7.4K]

Answer:

Question number 13 is 18

8 0

3 years ago

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Find the surface area of the triangular prism (above) using its net (below).

r-ruslan [8.4K]

Answer:

96 square units

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.

My answer:

The length of the large rectangle is: 5
The width of the large rectangle is: 7

=> Area of the large rectangle = length × width = 7*5 = 35 square units

The length of the middle rectangle is: 7
The width of the middle rectangle is: 4

=> Area of the middle rectangle = length × width = 7*4 = 28 square units

The length of the small rectangle is: 7
The width of the small rectangle is: 3

=> Area of the small rectangle = length × width = 7*3 = 21 square units

Area of top and the bottom triangles =2* $\frac{1}{2}bh$ $= 4*3 =12$

Total surface area = 35 + 28 + 21 + 12 = 96 square units

3 0

3 years ago

Read 2 more answers

Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

4 years ago

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

salantis [7]

Answer:

b =15

Step-by-step explanation:

We can use Pythagoras theorem to find b:

$a^{2}+b^{2} = c^{2}$