MATHEMATICS COLLEGE

Question:Fibonacci 1. Here are the first 5 terms of a quadratic sequence.
1
3
7
13
21
Find an expression, in terms of n for the nth term of this quadratic sequence.

Answers

Answer 1
Answer:

9514 1404 393

Answer:

  n² -n +1

Step-by-step explanation:

First differences of the terms of the sequence are ...

  3-1 = 2

  7-3 = 4

  13-7 = 6

  21-13 = 8

Second differences are ...

  4-2 = 2

  6-4 = 2

  8-6 = 2

In a quadratic sequence the coefficient of the squared term is half of the second difference value. Here, that means the squared term will be (2/2)n² = n².

__

We can find the other terms of the quadratic expression by considering the differences between n² and the actual sequence.

The sequence of n² terms is ...

  1, 4, 9, 16, 25

When we subtract these from the actual sequence, we get ...

  1-1 = 0

  3-4 = -1

  7-9 = -2

  13-16 = -3

  21-25 = -4

That is, the amount subtracted from n² is one less than the term number.

The expression for the n-th term is ...

  an = n² -n +1

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A certain human red blood cell has a diameter of 0.000007 meters which expression represents this diameter in meters in scientific notation

Answers

0.000007 in scientific notation is equal to 77^(-6) times 10
I think it’s 7 x 10^6

Let h be the function given by h(x) =x+x-2
²-1
We will investigate the behavior of
both the numerator and denominator of h(x) near the point where x = 1. Let
f(x)= x³ + x -2 and g(x)=x²-1. Find the local linearizations of f and g at a = 1,
and call these functions Lf(x) and Lg(x), respectively.
Lf(x) =
L₂(x) =
Explain why h(x) ≈
Lf(x)
Lg(x)
for a near a = 1.

Answers

Final answer:

The local linearizations of f(x) and g(x) at a = 1 are Lf(x) = 4x - 5 and Lg(x) = 2x - 2 respectively. The function h(x) ≈ Lf(x)/Lg(x) because the local linearizations provide a good approximation of the numerator and denominator of h(x) near x = 1.


Explanation:

The local linearization of a function at a given point is an approximation of the function using a linear equation. To find the local linearization of a function f at a = 1, we need to find the slope of the tangent line at a = 1, which is equivalent to finding the derivative of f at x = 1. By taking the derivative of f(x) = x³ + x - 2, we get f'(x) = 3x² + 1. Evaluating f'(1), we find that the slope of the tangent line at a = 1 is 4. Therefore, the local linearization of f at a = 1, denoted as Lf(x), is given by Lf(x) = f(a) + f'(a)(x - a), which becomes Lf(x) = -1 + 4(x - 1) = 4x - 5.

Similarly, to find the local linearization of g(x) = x² - 1 at a = 1, we need to find the slope of the tangent line at a = 1. The derivative of g(x) is g'(x) = 2x. Evaluating g'(1), we find that the slope of the tangent line at a = 1 is 2. Therefore, the local linearization of g at a = 1, denoted as Lg(x), is given by Lg(x) = g(a) + g'(a)(x - a), which becomes Lg(x) = 0 + 2(x - 1) = 2x - 2.

When investigating the behavior of the function h(x) = (f(x))/(g(x)) near the point x = 1, we can approximate h(x) using the local linearizations of f and g at a = 1. Near the point a = 1, h(x) ≈ Lf(x)/Lg(x) because Lf(x) and Lg(x) provide a good approximation of the numerator and denominator, respectively, of h(x). This approximation holds as long as x is close to 1.


Learn more about local linearizations of functions here:

brainly.com/question/34258619

HOT AIR BALLOON A balloon rises340 feet into the air. Then it descends

130 feet

PLEASE ANSWER I REALLY NEED IT

Answers

Answer:

it is at 210 feet

Step-by-step explanation:

it rises 340 feet, then it descends 130 so we subtract 130 from 340 which gets us 210 feet.

If you can simplify this equation to the final stage I will reward you!! Try you're best!! I will not give my points to people that don't deserve them :)

Answers

k = -18

you can solve for k by simplifying both sides of the equation, then isolating the variable.

k=9     soo  got 9 by adding 6 and 8 which equals 14 then i thought 14 minus what equals 5 and got 9 which is the answer for k.

According to the Centers or Disease Control and Prevention, 9.6% of high school students current through (c) below a (a) Determine the null and alternative hypotheses. (Type integers or decimals. Do not round.) (b) If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the high school counselor. 0 A. There is sufficient evidence to conclude that the proportion of high school students exceeds 0.096 at this counselors high school. O B. There is not sufficient evidence to conclude that the proportion of high school students exceeds 0.096 at this counselor's high school o c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O D There is not sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselors high school.

Answers

Answer:

c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O

Step-by-step explanation:

Given that according to the Centers or Disease Control and Prevention, 9.6% of high school students current through (c) below a

(a) Determine the null and alternative hypotheses.

H_0: p =0.096\nH_a : p >0.096

(right tailed test for proportion of high school students )

b) If the null hypothesis should not be rejected, state the conclusion of the high school counselor.

c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O

Do Dinosaurs Really Exist?

Answers

no they don't exist , people says that they used to but that long time ago 
Scientist are still trying to figure that out.
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