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2 years ago

9) Write an equation of the line that passes through the point (4, –5) with slope 2.

Mathematics

1 answer:

aleksklad [387]2 years ago

8 0

Answer:

Step-by-step explanation:

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Write seven hundred two and six hundred fifty-six thousandths in standard form and in expanded form.

Naddik [55]

Standard Form: 702.656
Expanded Form: 700+2+0.6+0.05+0.006

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3 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

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

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3 years ago

Which figure has only rotational symmetry

NikAS [45]

Its either A or B but my bets are on A

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3 years ago

Section J in an arena has 20 rows. Each row has 15 seats. Our tickets cost $18 each. If all the seats are sold, how much money w

Helga [31]

Section J has 20 rows....each row has 15 seats....so section J has (20 * 15) = 300 seats. If each seat costs $ 18, and all the seats are sold, then the amount of money collected would be : (300 * 18) = $ 5,400 <=

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3 years ago

Write the equation of the line in slope-intercept form using y=mx+b

natta225 [31]

Answer:

y = 4x + 4

Step-by-step explanation:

Two points you can see on the graph are (0,4) and (-2,-4)

Now, to find the slope, use delta y/ delta x

(-4-4)/(-2-0)

(-8)/(-2) = 4

Slope is 4.

y = 4x + b

Now, to find b, we need the y-intercept, which is the point where x is 0 and the graph crosses the y-axis.

This value is 4. So, the y-intercept is 4

Substitute into your equation

y = 4x + 4

6 0

2 years ago

Read 2 more answers