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Pavel
4 days ago
5

Choose the correct item from each drop-down menu to factor the trinomial 6y2 + 19y + 15 by grouping.

Mathematics
1 answer:
AnnZ [3.8K]4 days ago
5 0

Answer: (3y - 5) • (2y - 3)

Step-by-step explanation: 6y2 - 10y - 9y - 15

2.1 Factoring 6y2-19y+15

The leading term is 6y2, with a coefficient of 6.

The middle term is -19y, having a coefficient of -19.

The last term is the constant, which is +15.

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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
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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

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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=1.21g/day

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

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Answer:

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10 days ago
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According to the provided information, the talent show organizers have a budget of $1800 to purchase merchandise clothing for sale at the event. The price for shirts is $10 each, while hats are priced at $8.

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