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2 years ago

What is the maximum of the sinusoidal function?

Mathematics

1 answer:

Alex17521 [72]2 years ago

4 0

Answer:

The maximum of y = sin x is 1. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function.

Step-by-step explanation:

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PLEASE HELP! A S A P

sleet_krkn [62]

There should be 30 cars in the parking lot

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3 years ago

Sabe-se que f é uma função de proporcionalidade direta e que f(1)=4.

ad-work [718]

So this is french I don’t soeak it so ye

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3 years ago

Suppose Upper F Superscript prime Baseline left-parenthesis x right-parenthesis equals 3 x Superscript 2 Baseline plus 7 and Upp

Sedaia [141]

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

$F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt$

$F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt$

$F(x)=5+(t^3+7t)\bigg|_0^x$

$F(x)=5+x^3+7x$

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0) → F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1) → F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2) → F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5) → F (2.0) ≈ 20.164

4 0

3 years ago

In the expression “six to the power of four is 1,296," which number is the base?

cestrela7 [59]

Six is the base because 6^4 is 1296.

7 0

3 years ago

A semi- circle has an area of 35cm . What is its diameter?

patriot [66]

Answer:

<h2>Area Semicircle = 1/2 πr² </h2>

where

r radius of semicircle

→ ½ * 22/7 * r² = 35

→ 11/7 * r² = 35

→ r² = 35*7/11

→ r² = 245/11

→ r² = 22.77

→ r = √22.77

→ r = 4.77

Therefore,

Diameter = 2*4.77

= 9.54 cm

5 0

2 years ago