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3 years ago

What is 23 over 18 in simplest form

1 answer:

6 0

$\frac{23}{18}$ is already in simplest form because 23 is a prime number, which means that it is only divisible by 1 and itself (23). Hope this helps! :)

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Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial (1+3x)^(-1

PolarNik [594]

Answer:

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

Step-by-step explanation:

We are given that function

$f(x)=(1+3x)^{-1/3}$

We have to find the first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

$f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....$

$f(0)=(1+3x)^{\frac{-1}{3}}=1$

$f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}$

$f'(0)=-1$

$f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}$

$f''(0)=4$

$f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}$

$f'''(0)=-28$

Substitute the values we get

$(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...$

$(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...$

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

5 0

3 years ago

Find the 66th term of the arithmetic sequence -28,-45, -62,-

Alexeev081 [22]

Answer:

-1133

Step-by-step explanation:

Formula for nth term

aₙ = a + (n - 1)d

Finding d

d = -45 - (-28)
d = -45 + 28
d = -17

Solving for a₆₆

a₆₆ = -28 + 65(-17)
a₆₆ = -28 - 1105
a₆₆ = -1133

6 0

2 years ago

Read 2 more answers

Choose the system of equations which matches the following graph:

aleksandr82 [10.1K]

The coordinates give are
(0,6)
(4,9)

(3,6)
(2,3)

These points can be substituted into the systems of equation in the choices and inspect which equations satisfy the value of the points. Doing this, the answer is
3x - 4y = -24
3x - y = 3

4 0

3 years ago

Antonio needed a loan worth 5,600. If the bank calculates interest at 3.1% compounded semi annually how much does he owe in 3yea

Ket [755]

5600 in three yoears

3 0

3 years ago

Please help with this math

larisa86 [58]

I think it’s b ????

7 0

3 years ago

Read 2 more answers