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3 years ago

The vertex of this parabola is at (-3, 6). Which of the following could be its equation?

Mathematics

1 answer:

pishuonlain [190]3 years ago

6 0

Since the vertex is at (-3, 6), the equation is given by
y = a(x + 3) + 6

Therefore, option A is the correct answer.

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4 years ago

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What are the zeros of (x-2)(x^2-9)

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3 years ago

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Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

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3 years ago

Allison and Megan were at track practice. The track is 3/8 kilometers around.

Ad libitum [116K]

Allison ran 3/8 km (0.375 km) in 3 minutes.

Set up a proportion to find how long it takes for her to run 1 km

$\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}$

Cross multiply to get:

$3 = 0.375x$

Solve:

$x = \frac{3}{0.375}$

x = 8 minutes

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3 years ago

3 less than one-thirteenth of some number, w

Leviafan [203]

As an expression, it would be:

3 - 1/13w (or you could also do 1/13w - 3).

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3 years ago