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2 years ago

Expand and simplify bracket please quickly

Mathematics

1 answer:

natulia [17]2 years ago

4 0

Answer:

4y²-1/4 is the required answer

Step-by-step explanation:

$(2y - \frac{1 }{2} )(2y + \frac{1}{2} ) \\ using \: formula \: {x}^{2} - y {}^{2} = (x - y)(x + y) \\ 4y {}^{2} - \frac{1}{4}$

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Answer:

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3 years ago

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Find the value of p if Cos 49 = Sin(p+10)

timofeeve [1]

Answer:Do you mean find p? If so then p+10 = 90 - 49, so p = 31°. Another possibility is in the second quadrant where p + 10 = 180 - 41 so p = 129° (The 41 comes from the first p+10, i.e. 31+10 = 41),

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Step-by-step explanation:

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3 years ago

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial

xxTIMURxx [149]

Step-by-step explanation:

Let the initial population of a community be P0 and the population after time t is P(t).

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$P(t) = P_0e^{kt}$

at t = 5 years, P(t) = 2P0

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$2P_0 = P_0e^{5k}\\2 = e^{5k}\\ln2 = lne^{5k}\\ln2 = 5k\\k = \frac{ln2}{5}\\k = 0.1386$

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$9000 = P_0e^{0.1386\times 3}\\9000 = P_0e^{0.4158}\\9000 = 1.5156P_0\\P_0 = \frac{9000}{1.5156}\\ P_0 = 5938.24$

Hence the initial population is approximately 5938.

b) In order to know how fast the population growing at t = 10, we will substitute t = 10 into the formula as shown:

$P(10) = 5938.24e^{0.1386(10)}\\P(10) = 5938.24e^{1.386}\\P(10) = 5938.24(3.9988)\\P(10) = 23,745.97$

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4 years ago

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nadezda [96]

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3 years ago

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melamori03 [73]

Answer:

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Step-by-step explanation:

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