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aev [14]
3 years ago
10

Identify the graph of 3x^2+y^2=9 for T(-1,3) and write an equation of the translated or rotated graph in general form.

Mathematics
2 answers:
Archy [21]3 years ago
8 0

ANSWER

D. Ellipse;

3{x}^{2}  +{y}^{2}  + 6x   - 6y + 3= 0

EXPLANATION

The given equation is

3 {x}^{2}  +  {y}^{2}  = 9

Dividing through by 9 gives

\frac{ {x}^{2} }{ 3}  +  \frac{ {y}^{2} }{9}  = 1

This is the equation of an ellipse centered at the origin.

If this ellipse has been translated, so that its center is now at (-1,3), then the equation of the translated ellipse becomes

\frac{ {(x + 1)  }^{2} }{ 3}  +  \frac{ {(y - 3)}^{2} }{9}  = 1

We multiply through by 9 to get,

3 {(x + 1)}^{2}  +  {(y - 3)}^{2}  = 9

Expand to obtain;

3( {x}^{2}  + 2x + 1) +  {y}^{2}  - 6y + 9 = 9

Expand to obtain;

3{x}^{2}  + 6x + 3+  {y}^{2}  - 6y + 9 = 9

Regroup and equate to zero to obtain;

3{x}^{2}  +{y}^{2}  + 6x   - 6y + 3= 0

kipiarov [429]3 years ago
6 0

Answer:

ANSWER

D. Ellipse;

just took the test on edgen.

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Suppose three marksmen shoot at a target. The ith marksman fires ni times, hitting the target each time with probability Pi, ind
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Let X represent the time it takes from when someone enters the line for a roller coaster until they exit on the other side. Cons
Yuri [45]

Answer:

a. E(x) = 3.730

b. c = 3.8475

c. 0.4308

Step-by-step explanation:

a.

Given

0 x < 3

F(x) = (x-3)/1.13, 3 < x < 4.13

1 x > 4.13

Calculating E(x)

First, we'll calculate the pdf, f(x).

f(x) is the derivative of F(x)

So, if F(x) = (x-3)/1.13

f(x) = F'(x) = 1/1.13, 3 < x < 4.13

E(x) is the integral of xf(x)

xf(x) = x * 1/1.3 = x/1.3

Integrating x/1.3

E(x) = x²/(2*1.13)

E(x) = x²/2.26 , 3 < x < 4.13

E(x) = (4.13²-3²)/2.16

E(x) = 3.730046296296296

E(x) = 3.730 (approximated)

b.

What is the value c such that P(X < c) = 0.75

First, we'll solve F(c)

F(c) = P(x<c)

F(c) = (c-3)/1.13= 0.75

c - 3 = 1.13 * 0.75

c - 3 = 0.8475

c = 3 + 0.8475

c = 3.8475

c.

What is the probability that X falls within 0.28 minutes of its mean?

Here we'll solve for

P(3.73 - 0.28 < X < 3.73 + 0.28)

= F(3.73 + 0.28) - F(3.73 + 0.28)

= 2*0.28/1.3 = 0.430769

= 0.4308 -- Approximated

5 0
3 years ago
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