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3 years ago

What equation passes through (0,5) and (-4,-1)

Mathematics

1 answer:

kogti [31]3 years ago

7 0

Answer: y = 3/2x + 5

Step-by-step explanation:

Find the slope/gradient:

$\frac{-1-5}{-4-0} = \frac{-6}{-4} = \frac{3}{2}$

Plug in a point to the equation:

$5 = \frac{3}{2}(0) + b$

Solve for b:

$5 = b$

New equation:

$y = \frac{3}{2}x + 5$

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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

Jenn equally shares 40 jellybeans with some friends. Is the number that each friends gets greater than 40 or less than 40? Expla

blagie [28]

I would say that it would be less than. The question says Jenn shared a total of 40 jellybeans equally and to share with others, Jenn would have to divide the jellybeans among her friends. Since she is dividing the jellybeans, the amount each friend gets would be less than the total. Therefore it would be less than 40.

6 0

2 years ago

I need help on this one please

saw5 [17]

Answer:

Step-by-step explanation:

When looking at the number line, we can see the distance between A and B is one unit

A |-2| + |-1| = 2+1 =3 That is not 1 unit

B 2-1 =1 that is 1 unit

C -2 + -1 = -3 that is not 1 unit

D |-1| - (-2) = 1 + 2 =3 that is not 1 unit

Even though it says all expressions, there is only 1 that shows a distance of 1 unit

6 0

3 years ago

What is the sum of 2 + 3i and −1+7i<br> A 1 + 10i<br> B 3−4i<br> C 5 + 6i<br> D 9 + 2i

poizon [28]

A is the correct answer

2 + 3i + (-1) + 7i
1 + 10i

6 0

3 years ago

Read 2 more answers

A farmer sells eggs in containers holding a dozen eggs. If he has 2178 eggs, how many containers will be filled completely? How

BARSIC [14]

Answer:

~181 containers filled completely, 6 eggs left over

Step-by-step explanation:

2178 ÷ 12 (a dozen, the number of eggs per container) = 181.5 containers

181 × 12 = 2,172 eggs

2,178 eggs - 2,172 = 6 eggs left over

3 0

2 years ago