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2 years ago

I really really need help guys!

Mathematics

1 answer:

Degger [83]2 years ago

7 0

Answer:

area of the figure=1/2×16×7

=56 m²

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A hat factory makes 2 types of hats. Each day, the factory makes 400 of each type of hat. How many hats does the factory make ea

Lostsunrise [7]

The factory makes a total of 800 hats

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2 years ago

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

A stadium has seating accommodation for 3800 people. At a cricket match all seats were taken. If there were 5609 people attendin

umka2103 [35]

Answer:

Step-by-step explanation:

Those standing is the same thing as people who didn't have seats.

Those standing = the total number of people attending - those seated.

Those standing = 5609 - 3800

Those standing = 1809

6 0

2 years ago

Work out the area of this circle.

exis [7]

We know that

Area of circle = πr²

=> π × (6)²

=> π × 36

=> 36π mm²

3 0

2 years ago

Read 2 more answers

PLEASE HELP ME!! I NEED TO GET THIS DONE

Rainbow [258]

Answer:

Step-by-step explanation:

Dilation. Since it's only the size of the figure that's changing

Height of the smaller one: 4

Width of the smaller one: 6

Height of the bigger one: 6

Width of the bigger one: 9

6/4 = 1.5

9/6 = 1.5

Since both 6/4 and 9/6 was 1.5, that means that the Width and Height was proportional and that the two trapezoids is at a ratio o:

1 : 1.5

One unit of the smaller one is 1.5 units on the bigger one.

5 0

2 years ago