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2 years ago

Using the graph to the right, write the ratio in simplest form. BD/AD

Mathematics

1 answer:

Romashka [77]2 years ago

6 0

Answer:

$\frac{BD}{AD} = \frac{5}{7}$

Step-by-step explanation:

Coordinate of B = 1

Coordinate of D = 6

Coordinate of A = -1

BD = |1 - 6| = 5 units

AD = |-1 - 6| = |-7| = 7 units

$\frac{BD}{AD}$

Plug in the values

$\frac{BD}{AD} = \frac{5}{7}$

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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

3 years ago

When solving the system of equations by graphing, what is the solution of 3x + 2y = 2 and 2x – y=6?

oksian1 [2.3K]

Answer:

answer B: (2,-2)

Step-by-step explanation:

First, write the equations on top of each other:

$3x+2y=2\\2x-y=6$

Then, multiply the the second equation by 2 so that we can use elimination of the y-variable:

$3x+2y=2\\2(2x-y)=2(6)\\\\3x+2y=2\\4x-2y=12$

Next, use elimination to find the value of "x":

$3x+2y=2\\+(4x-2y=12)\\\\7x+0=14\\7x=14\\\frac{7x}{7}=\frac{14}{7}\\x=2$

So, your x-value is 2.

Now, substitute your x-value into one of your equations, let's take the second equation, 2x-y=6:

$2x-y=6\\2(2)-y=6\\4-y=6\\4-4-y=6-4\\-y=2\\\frac{-y}{1}=\frac{2}{-1}\\y=-2$

Your y-value is -2.

With all your information gathered, you find that the solution to this system of equation is (2,-2).

5 0

3 years ago

Heyy! i’ll give brainliest please help.

san4es73 [151]

Answer:

The answer is B.

Step-by-step explanation:

Its B because the lower the altitude the higher the pressure, and in this case the air towards the ground is being moved up, which is letting cold air sink back down.

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Answer:

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Step-by-step explanation:

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3 years ago

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jonny [76]

Answer:

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Step-by-step explanation:

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