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2 years ago

If p − 1 is a factor of p4 + p2 + p − k, the value of k is

Mathematics

2 answers:

VashaNatasha [74]2 years ago

8 0

Answer:

k=3

Step-by-step explanation:

s2008m [1.1K]2 years ago

5 0

P-1 is a factor.
∴p=1 is one of the root of p⁴ + p² + p -k
f(p) = p⁴ + p² + p - k
∴ f(1) = 1⁴ + 1 ² + 1 - k = 0
∴ k = 3

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A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred

Paha777 [63]

Answer:

Step-by-step explanation:

Treat this like compound interest: Use A = P(1 + r)^t.

Here, P is the initial population and A is 3 times that, or 3P. Since P = 20 people, 3P = 60 people,

and this population is reached after 100 years.

We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.

60 = 20(1 + r)^100

Simplifying, 3 = (1 + r)^100.

Taking the natural log of both sides,

ln 3 = 100 ln (1 + r), or

ln 3

ln (1 + r) = ---------------

100

= 1.0986 / 100 = 0.01986

We must solve this for r. Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:

1 + r = 3, so r must = 2.

Now find the pop of the village today. Use the same equation: A = P (1+r)^t.

A = 20(1 +2)^4 (hundreds),

A = 20(3)^4, or

A = 81

The population after 400 years is 81.

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2 years ago

How does the range of g(x)=6/x compare with the range of the parent function (f)=1/x?

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2 years ago

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Answer:

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