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2 years ago

Complete the square for x^2+12x-5.

Mathematics

1 answer:

Setler [38]2 years ago

3 0

Answer:

$x^2+12x-5=(x+6)^2-41$

Step-by-step explanation:

The given expression is $x^2+12x-5$

Comparing to $ax^2+bx+c$ , we have $a=1,b=12,c=-5$

We add and subtract $(\frac{b}{2a})^2$

$x^2+12x+6^2-6^2-5$

This implies that:

$\boxed{x^2+6x+36}-36-5$

The expression in the rectangle is a perfect square

$(x+6)^2-41$

Therefore $x^2+12x-5=(x+6)^2-41$

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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:

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

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

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

$P(\infty) = 1200$

5 0

2 years ago

Someone please help! Thxx

tangare [24]

Answer:

E, needs more info to be determined

Step-by-step explanation:

We know that Kai takes 30 minutes round-trip to get to his school.

One way is uphill and the other is downhill.

He travels twice as fast downhill than uphill.

This means that uphill accounts for 20 minutes of the round-trip and downhill accounts for 10 minutes of his trip.

However, even with this information, we do not know how far his school is.

In order to figure out how far away his school is, we would need more information about the speed at which Kai is traveling.

Simply knowing that he travels twice as fast downhill is not enough.

This question could only be solved by knowing how many miles Kai travels uphill or downhill in a given time.

3 0

2 years ago

Simone builds a simple spinning engine by inserting straws through holes in a plastic cup. She then suspends the cup from a meta

Zinaida [17]

D. It is smaller In magnitude

3 0

2 years ago

What is the equation of a vertical line passing through the point (−4, 7)? y = 7 y = −4 x = 7 x = −4

Katen [24]

The equation of the vertical line passing through point -4,7 would be X = -4.

8 0

2 years ago

Read 2 more answers

-1/7 is greater than all of the follwing except

sergejj [24]

Answer:

0.1 is -1/10 which is obviously less than -1/7 .

Else we can also know by multiplying by 100

-1/10 *100 = -10

-1/7 *100 = -14.444

5 0

2 years ago