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3 years ago

Define the axis of symmetry, vertex, focus and directrix for

Mathematics

1 answer:

Papessa [141]3 years ago

8 0

Answer:

see attached

Step-by-step explanation:

The equation is in the form ...

4p(y -k) = (x -h)^2 . . . . . (h, k) is the vertex; p is the focus-vertex distance

Comparing this to your equation, we see ...

p = 4, (h, k) = (3, 4)

p > 0, so the parabola opens upward. The vertex is on the axis of symmetry. That axis has the equation x=x-coordinate of vertex. This tells you ...

vertex: (3, 4)

axis of symmetry: x = 3

focus: (3, 8) . . . . . 4 units up from vertex

directrix: y = 0 . . . horizontal line 4 units down from vertex

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Suppose N has a geometric distribution with parameter p. Derive a closed-form expression for E(N | N <= k), k = 1,2,... Check

vfiekz [6]

Answer:

P(X= k) = (1-p)^k-1.p

Step-by-step explanation:

Given that the number of trials is

N < = k, the geometric distribution gives the probability that there are k-1 trials that result in failure(F) before the success(S) at the kth trials.

Given p = success,

1 - p = failure

Hence the distribution is described as: Pr ( FFFF.....FS)

Pr(X= k) = (1-p)(1-p)(1-p)....(1-p)p

Pr((X=k) = (1 - p)^ (k-1) .p

Since N<=k

Pr (X =k) = p(1-p)^k-1, k= 1,2,...k

0, elsewhere

If the probability is defined for Y, the number of failure before a success

Pr (Y= k) = p(1-p)^y......k= 0,1,2,3

0, elsewhere.

Given p= 0.2, k= 3,

P(X= 3) =( 0.2) × (1 - 0.2)²

P(X=3) = 0.128

3 0

3 years ago

Use the limit theorem and the properties of limits to find the horizontal asymptotes of the graph of the function g(x) = x2/x2-2

ElenaW [278]

Answer:

Option b is right.

Step-by-step explanation:

A function is given as

$g(x) = \frac{x^2}{x^2-2x-1}$

Limit is to be found out for x tends to infinity.

We find that numerator and denominator has the same degree.

HEnce a horizontal asymptote exists

COefficients of leading terms are 1 and 1 respectively

Asymtote would be y =1/11 = 1

Alternate method:

When x tends to infinity, 1/x tends to 0

$g(x) =\frac{\frac{1}{x^2} }{1-\frac{2}{x} -\frac{1}{x^2} }$

by dividing both numerator and denominator by square of x.

Now take limit as 1/x tends to 0

we get

limit is y tends to 1/1 =1

Hence horizontal asymptote is y =1

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4 years ago

Given rectangular prism ABCD.

Lana71 [14]

B and d are tge answers

4 0

3 years ago

Read 2 more answers

Order the set of number from least to greatest .

earnstyle [38]

Answer (Please vote me Brainliest if this helps!):

The answer is D

Step-by-step explanation:

Lets start off with the square roots:

$\sqrt{16}$ = 4

$\sqrt{18}$ = $3\sqrt{2}$ = 4.24264...

Mixed fraction:

$4\frac{2}{3}$ = 4.667

Therefore the answer is D.

6 0

3 years ago

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1. -6(9 - 9v)<br> 2. -8(b + 3)<br> 3. -(3x - 9)

never [62]

Answer:

1) =54v−54

−6(9−9v)

=(−6)(9+−9v)

=(−6)(9)+(−6)(−9v)

=−54+54v

=54v−54

2) =−8b−24

−8(b+3)

=(−8)(b+3)

=(−8)(b)+(−8)(3)

=−8b−24

3) −(3x−9)

=−3x+9

Step-by-step explanation: Hope this help :D

5 0

3 years ago