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3 years ago

Graph g(x)=2+|x| and it’s parent functions

Mathematics

1 answer:

matrenka [14]3 years ago

8 0

The parent function is ...

... f(x) = |x|

This is the absolute value function, equal x when x ≥ 0, and equal to -x when x < 0. Its graph has the shape of a V with the vertex at the origin and "legs" of slope ±1.

The function g(x) is the same function with 2 added. The addition of 2 moves every value of f(x) up 2 units, so translates the whole graph upward by 2 units.

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Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

What equation represents a line that is parallel to the line y=3-2x

GarryVolchara [31]

The line whose equation is

y = (any number) - 2x

is parallel to the line y = 3 - 2x , because they have the same slope.

6 0

3 years ago

X/7- y/5=1 solve for y

Usimov [2.4K]

Answer:

y = 5/7 x -5

Step-by-step explanation:

X/7- y/5=1

Multiply each side by 35 to clear the fractions

35(X/7- y/5) =1*35

5x - 7y = 35

Subtract 5x from each side

5x-5x-7y = -5x+35

-7y = -5x+35

Divide each side by -7

-7y/-7 = -5x/-7 +35/-7

y = 5/7 x -5

4 0

3 years ago

Read 2 more answers

What is the truth value for the following conditional statement?

Studentka2010 [4]

Answer:

TT→T

Step-by-step explanation:

If p is false, then ~p is true.

If q is false, then ~q is true.

Now note that

If a and b are both true, then a→b is true.
If a is true, b is false, then a→b is false.
If a is false, b is true, then a→b is true.
If a and b are both false, then a→b is true.

In your case, both~p and ~q are true, then ~p→~q is true too (or TT→T)

3 0

3 years ago

X-2y=10 x+3y=5 please hellppppppp

Marta_Voda [28]

Answer:

x=8,y=-1

Step-by-step explanation:

x-2y=10

x=10+2y

10+2y+3y=5

5y=-5

y=-1

x-2(-1)=10

x=8

3 0

3 years ago

Read 2 more answers