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3 years ago

X^2-8x+6 in vertex form

Mathematics

1 answer:

kompoz [17]3 years ago

4 0

$x^2-8x+6=\\
x^2-8x+16-10=\\
(x-4)^2-10$

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Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.

vekshin1

$x^2+y^2+z^2=100z\iff x^2+y^2+(z-50)^2=50^2$

The surface of interest can be parameterized by

$\mathbf r(u,v)=\begin{cases}x(u,v)=50\cos u\sin v\\y(u,v)=50\sin u\sin v\\z(u,v)=50(\cos v+1)\end{cases}$

with $0\le u\le2\pi$ and $0\le v\le\arccos\dfrac{49}{50}$ .

The area of the surface $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm dA=\iint_T\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv$

We have

$\|\mathbf r_u\times\mathbf r_v\|=50^2\sin v$

so the area is given by the double integral

$\displaystyle50^2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\arccos(49/50)}\sin v\,\mathrm dv\,\mathrm du=100\pi$

6 0

3 years ago

Which of the sets of ordered pairs represents a function? (5 points) A = {(2, −2), (5, −5), (−2, 2), (−5, 5)} B = {(4, 2), (4, −

ELEN [110]

Answer:

Step-by-step explanation:

6 0

2 years ago

Given the equation 2x − 5 = 8, which order of operations completely solves for x?

blagie [28]

2x - 5 = 8 Add 5 on both sides

2x - 5 + 5 = 8 + 5

2x = 13 Divide 2 on both sides to get "x" by itself

x = $\frac{13}{2}$

So addition and division

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3 years ago

A rectangle has the sum of length and breadth 20 cm. find the perimeter.

kupik [55]

<h2>Answer:</h2>

40 cm.

<h2>Step-by-step explanation:</h2>

$Because=(long+width)\times 2=perimeter$

$50:the\ perimeter=20\times 2=40\ cm$

<em>I hope this helps you</em>

4 0

2 years ago

For all values of x, f(x) = x^2 + 1 and g(x) = x-5

Elena-2011 [213]

Answer:

a) f g(x) = x³ - 5 x² + x -5

b) g(f(x) = x³ - 5 x² + x -5

Step-by-step explanation:

Given that f(x) = x² + 1 and g(x) = x-5

f(g(x)) = f(x-5) = (x-5)²+1 = x² - 10x +25 +1 = x² - 10 x +26

a) f g(x) = f(x) g(x) = (x² + 1 )(x-5) = x³ - 5 x² + x -5

b) g(f(x) = g(x) f(x) = (x-5) (x²+1) = x³ - 5 x² + x -5

6 0

2 years ago