I need help with this please

Using the given information, give the vertex form equation of each parabola.

Amanda [17]

Answer:

The equation of parabola is given by : $(x-4) = \frac{-1}{3}(y+3)^{2}$

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:( $\frac{47}{12}$ ,-3)

The general equation of parabola is given by.

$(x-h)^{2} = 4p(y-k)$ , When x-componet of focus and Vertex is same

$(x-h) = 4p(y-k)^{2}$ , When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

For value of p:

p= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

p= $\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}$

p= $\sqrt{(\frac{1}{12})^{2}}$

p= $\frac{1}{12}$ and p= $\frac{-1}{12}$

Since, Focus is left side of the vertex,

p= $\frac{-1}{12}$ is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p= $\frac{-1}{12}$

$(x-h) = 4p(y-k)^{2}$

$(x-4) = 4(\frac{-1}{12})(y+3)^{2}$

$(x-4) = \frac{-1}{3}(y+3)^{2}$

8 0

3 years ago

Determine the exact value of sin 13pi/12

ohaa [14]

To answer the problem above, convert the given angle to an equivalent angle with the unit of degrees.
(13π / 12 rad) x (360° / 2π) = 195°
We can solve this by directly inputting the value in our scientific calculators. The answer is approximately -0.2588.

6 0

3 years ago

Can someone please help me with these math problems ASAP?! Thanks in advance! ;)

Mamont248 [21]

Answer:

11) Here given Function,

$f(x) = \sqrt{2x-11}$

And, $g(x) = -|0.1|x+5$

For f(x) = g(x)

$\sqrt{2x-11}=-|0.1|x+5$

$2x-11=(-|0.1|x+5)^2$

$2x-11=0.01x^2 - 10|0.1|x+25$

$2x=0.01x^2 - 10|0.1|x+25+11$

$2x=0.01x^2 - 10|0.1|x+36$

$0.01x^2 - 10|0.1|x - 2x+36=0$

When we solve this equation,

We found,

x = 12.5227 ≈ 12.53

Thus, the required solution is, x = 12.53

12) Here the height of rocket A in x second,

$f(x) = -16x^2+74x+9$

And, The height gain by the rocket B in x seconds,

$g(x) = -16x^2+82x$

If at x seconds both A and B gain the same height,

That is, f(x) = g(x)

⇒ $-16x^2+74x+9= -16x^2+82x$

⇒ $74x + 9 = 82x$

⇒ $82x - 74x = 9$

⇒ $8x = 9$

⇒ x = 1.125 ≈ 1.13

Thus, the required solution is x = 1.13 seconds (approx)

4 0

2 years ago

2 2. Evaluate (a + y)+ 2y if a = 5 and y = -3. F 58 G -2 H 70 J 10

NARA [144]

<h3>Answer: G) -2</h3>

=======================================================

Explanation:

I'm assuming you meant to say (a+y)^2 + 2y

Replace each copy of 'a' with 5. Replace each copy of 'y' with -3. Use PEMDAS to simplify.

(a+y)^2 + 2y

(5 + (-3))^2 + 2(-3)

(5-3)^2 + 2(-3)

(2)^2 + 2(-3)

4 + 2(-3)

4 - 6

-2

So (a+y)^2 + 2y = -2 when a = 5 and y = -3.

3 0

2 years ago

How was FDR a lasting impact on today's society?

Gre4nikov [31]

Answer:

He created numerous programs to provide relief to the unemployed and farmers while seeking economic recovery with the National Recovery Administration and other programs

He also instituted major regulatory reforms related to finance, communications, and labor, and presided over the end of Prohibition

Step-by-step explanation:

Hope this helps:)

7 0

2 years ago