What expression is equivalent to 5(6x + 3y)

A line passes through the points (-4,1) and (-3,3). This line can be modeled by the equation y

skelet666 [1.2K]

Answer:

A

Step-by-step explanation:

6 0

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

3 years ago

Magnitude statistics allow one to draw general conclusions about a population from information collected in a population sample.

kow [346]

inferential statistics allows for someone to draw conclusions about a population from the information collected in a population sample.

the qestion is incomplete .please read below to find the missing content

Which of the following allows for someone to draw conclusions about a population from the information collected in a population sample?

a. magnitude statistics

b. central tendency

c. inferential statistics

d. effect size

The population is the number of people living together in a place. The population of a city is the number of people living in that city. These people are called residents or residents. The population includes all individuals living in that particular area.

Population refers to the total number of organisms living in a particular area. Population helps us estimate the number of beings and know how to act accordingly. For example, knowing the exact population of a city allows us to estimate the number of resources required. Similarly, animals can do the same.

Learn more about the population here

brainly.com/question/25896797

#SPJ4

5 0

1 year ago

The angles of elevation froma point X to the top of flagpoles A and B are 35* and 45* respectively. If X lies in the middle of t

BartSMP [9]

Let AB = t. And since X lies in the middle, so AX=BX = t/2 .

Let the height of the smaller flagpole is AO and of larger flagpole is BP .

Using tangent ratio rule in each triangle, we will get

$tan 35 =\frac{AO}{t/2} , tan 45= \frac{BP}{t/2} // AO = \frac{t*tan35}{2}, BP=\frac{t*tan45}{2}$

And there ratio is

$\frac{AO}{BP}= \frac{tan 35}{tan 45}=\frac{0.7}{1}$

5 0

2 years ago

Find the length of a to the nearest tenth using the Pythagorean theorem

Leona [35]

Answer:

Ab^2 = CA^2 + BC^2

8^2 = 6^2 + a^2

64 = 36 + a^2

64-36 = a^2

28 = a^2

square root of 28 = square root of a^2

5 ,29 = a

5 = a

8 0

2 years ago