dumnealorjavgj
2022-05-08
Answered

x^4-4

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necrologo9yh43

Answered 2022-05-09
Author has **23** answers

Exact Form:x=√2,−√2

Decimal Form:x=1.41421356,−1.41421356

Decimal Form:x=1.41421356,−1.41421356

asked 2021-03-02

Write A if the sequence is arithmetic, G if it is geometric, H if it is harmonic, F if Fibonacci, and O if it is not one of the mentioned types. Show your Solution.
a. $\frac{1}{3},\frac{2}{9},\frac{3}{27},\frac{4}{81},...$
b. $3,8,13,18,...,48$

asked 2020-11-29

Prove the Arithmetic-Geometric Mean Inequality
If $a}_{1}{a}_{2},\dots ,{a}_{n$ are nonnegative numbers, then their arithmetic mean is $\frac{{a}_{1}+{a}_{2}+\dots +{a}_{n}}{n},$ and their geometric . The avthmetic-geometic mean is $\sqrt{n}\{{a}_{1},{a}_{2},\dots {a}_{n}\}.$ The arithmetic-geometric mean equality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers andy.
(a) If x and y are nonnegative and $x\le y,then{x}^{2}\le {y}^{2}.$
[Hint: First use Rule 3 of Inequalities to show that ${x}^{2}\le xy{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}xy\le {y}^{2}.$ ]
(b) Prove the arithmetic-geometric mean inequality $\sqrt{xy}\le \frac{x+y}{2}$

asked 2022-01-30

What is the leading term, leading coefficient, and degree of this polynomial $-5{x}^{4}-5{x}^{3}-3{x}^{2}+2x+4$ ?

asked 2021-09-30

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify.

asked 2021-02-11

Several models have been proposed to explain the diversification of life during geological periods. According to Benton (1997), The diversification of marine families in the past 600 million years (Myr) appears to have followed two or three logistic curves, with equilibrium levels that lasted for up to 200 Myr. In contrast, continental organisms clearly show an exponential pattern of diversification, and although it is not clear whether the empirical diversification patterns are real or are artifacts of a poor fossil record, the latter explanation seems unlikely. In this problem, we will investigate three models fordiversification. They are analogous to models for populationgrowth, however, the quantities involved have a differentinterpretation. We denote by N(t) the diversification function,which counts the number of taxa as a function of time, and by rthe intrinsic rate of diversification.

(a) (Exponential Model) This model is described by

(b) (Logistic Growth) This model is described by

(c) Assume that

(d) Use your answer in (c) to explain the following quote from Stanley (1979): There must be a general tendency for calculated values of

(e) Explain why the exponential model is a good approximation to the logistic model when

asked 2021-01-02

The half - life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth.

asked 2022-05-09

Simplify: 606-496.