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3 years ago

5

The answer to the problem plz

1 answer:

Vlad1618 [11]3 years ago

4 0

B I think hope you do good

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Which of the following is the standard equation of the ellipse with vertices at (1,0) and (27,0) and an eccentricity of 5/13?

Dovator [93]

The equation of the elipse is given by:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

The equation of an elipse of center $(x_0, y_0)$ is given by:

$\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 0$

Values a and b are found according to the <u>vertices and the eccentricity</u>.

It has vertices at (1,0) and (27,0), thus:

$x_0 = \frac{27 + 1}{2} = 14$

$y_0 = \frac{0 + 0}{2} = 0$

$a = \frac{27 - 1}{2} = 13$

$a^2 = 169$

It has eccentricity of $\frac{5}{13}$ , thus:

$\frac{5}{13} = \frac{c}{a}$

$\frac{5}{13} = \frac{c}{13}$

$c = 13$

Thus, b is given according to the following equation:

$c^2 = a^2 - b^2$

$b^2 = a^2 - c^2$

$b^2 = 169 - 25$

$b = \sqrt{144}$

$b = 12$

The equation of the elipse is:

$\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1$

A similar problem is given at brainly.com/question/21405803

3 0

3 years ago

The population of bacteria in a petri dish doubles every 24 h. The population of the bacteria is initially 500 organisms. How lo

liberstina [14]

Answer:

16.34 hours

Step-by-step explanation:

According to the given information we can see that the case is of exponential growth

Hence, we will use the formula

$A=P(2)^\frac{t}{24}$

Here A =800 is the amount that is needed to reach

P is the initial amount that is 500

We have to find the time it will take to reach 800 that is we need to find t

On substituting the values in the formula we get

$800=500(2)^\frac{t}{24}$

On simplification we get

$\Rightarrow\frac{8}{5}=(2)^\frac{t}{24}$

Taking log on both sides we get

$\Rightarrow\log\frac{8}{5}=\log(2)^\frac{t}{24}$

using $\log\frac{m}{n}=\log m-\log n$

And $\log a^m=m\log a$

$\Rightarrow\log{8}-\log{5}=\frac{t}{24}\log2$

Now substituting values of log 8=0.903, log 5=0.698 and log 2=0.301 we get

$\Rightarrow 0.903-0.698=\frac{t}{24}0.301$

$\Rightarrow 0.205=\frac{t}{24}0.301$

$\Rightarrow \frac{0.205}{0.301}\cdot 24=t$

$\Rightarrow t=16.34$

8 0

3 years ago

Read 2 more answers

Solve the equation<br> -18 + 24 = -2(x+6)

anzhelika [568]

Answer:

x = -9

Step-by-step explanation:

-18+24 = -2(x+6) Distribute and simplify

6 = -2x-12 Add 12 to both sides

18 = -2x Divide by -2 on both sides

-9 = x Here's your answer

Hope this helps! :D

3 0

2 years ago

Read 2 more answers

Which is equivalent to 1.04?

Elodia [21]

Answer:

104/100 is equivalent to 1.04

Step-by-step explanation:

7 0

3 years ago

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Rachel drove 756 miles in 12 hours.<br> At the same rate, how many miles would she drive in 8 hours?

kvv77 [185]

Answer:

504 miles

Step-by-step explanation:

you would do 756÷12 which equals 63.... For every hour that you drive its 63 miles. Then you do 63×8 to get 504

4 0

3 years ago