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10 days ago

Which graph has the same end behavior as the graph of f(x) = –3x3 – x2 + 1?

2 answers:

4 0

Without specific options available, I can provide guidance on where to focus your attention.

The end behavior of a function refers to how the graph behaves (upwards or downwards) as it nears positive or negative infinity within its domain. Essentially, we’re investigating the direction the graph tends towards on both sides.

In this scenario, as the value of x grows, the graph descends, while it ascends when x diminishes. Seek out a comparable occurrence.

lawyer [4K]10 days ago

4 0

The correct response to the question is D.

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A water sprinkler uses 12.9 gallons of water per minute. How many gallons of water will it use in 36.5 minutes?

lawyer [4008]

Answer: 470.85 gallons

Step-by-step explanation:

12.9 gal/min multiplied by 36.5 min equals 470.85 gal

4 0

4 days ago

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The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan^−1.(t/2), where t is measured in d

AnnZ [3877]

Answer:

1.21 g/day

Step-by-step explanation:

We start with the fact that

The mass of the bacterial colony (in grams) is described by

$P(t)=2+5tan^{-1}(\frac{t}{2})$

Where t=Time(in days)

Next, we differentiate with respect to t

$P'(t)=5(\frac{1}{1+\frac{t^2}{4}}\times \frac{1}{2})$

Using the formula $\frac{d(tan^{-1}(x)}{dx}=\frac{1}{1+x^2}$

$P'(t)=\frac{5}{2}(\frac{4}{4+t^2})$

$P'(t)=\frac{10}{4+t^2}$

We know that P(t)=6

Now, substitute this value

$6=2+5tan^{-1}(\frac{t}{2})$

$5tan^{-1}(\frac{t}{2})=6-2=4$

$tan^}{-1}(\frac{t}{2})=\frac{4}{5}$

$\frac{t}{2}=tan(\frac{4}{5})$

$t=2tan(\frac{4}{5})$

Insert the given value of t

$P'(2tan\frac{4}{5})=\frac{10}{4+4tan^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{10}{4}\times \frac{1}{1+tan^2(\frac{4}{5})}$

We understand that $1+tan^2\theta=sec^2\theta$

Applying the formula

$P'(2tan(\frac{4}{5})=\frac{5}{2}\times \frac{1}{sec^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times cos^2(\frac{4}{5})$

By employing $cos^2x=\frac{1}{sec^2x}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times (0.696)^2=1.21$ g/day

Consequently, the instantaneous rate at which the mass of the colony changes is=1.21g/day

7 0

11 days ago

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Which equation is y = 6x2 + 12x – 10 rewritten in vertex form?

lawyer [4008]

Y = 6 x² + 12 x - 10. Factor out the 6 to get 6 ( x² + 2 x ) - 10. Rewrite the quadratic by adding and subtracting 1 inside the parentheses: 6 ( ( x² + 2 x + 1 ) - 1 ) - 10.
This reduces to 6 ( x + 1 )² - 6 - 10 = 6 ( x + 1 )² - 16 ( vertex form)

5 0

13 days ago

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A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be i

Zina [3914]

Answer:

3/(30×30×30) = 3/27000 = 0.0001 or 0.01%

Step-by-step explanation:

3 0

12 days ago

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Alicia can choose 2 of her 5 best friends to go with her to the amusement park. Her best friends are Connie, Dale, Eric, Finley,

AnnZ [3877]

Answer:

Step-by-step explanation:

5/2= 2.5 (which can also be represented as 2 1/2 or 250%, depending on preference). However, since you can't have half a person entering the amusement park, we round down to the nearest whole number (2.5 → 2).

Hence, the final answer is 2.

6 0

1 day ago