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3 years ago

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A recipe calls for 1/4 cup of chicken broth and 2/6 cup of vegetable broth. what is the total amount of broth needed for the rec

ipe. what is the answer in simplest terms

1 answer:

Komok [63]3 years ago

7 0

7/12 because you gave to find a common denominator which is 12.

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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

2 years ago

Please help it’s finding sin C , cos C and tan C

Aloiza [94]

The given triangle has a right angle.

We use the mnemonics SOH-CAH-TOA.

1i) $\sin C =\frac{Opposite}{Hypotenuse}$ , $\implies \sin C =\frac{30}{34}$ , $\implies \sin C =\frac{15}{17}$

ii) $\cos C =\frac{Adjacent}{Hypotenuse}$ , $\implies \cos C =\frac{16}{34}$ , $\implies \cos C =\frac{8}{17}$

$\tan C =\frac{Opposite}{Adjacent}$ , $\implies \tan C =\frac{30}{16}$ , $\implies \tan C =\frac{15}{8}$

2. We want to find the hypotenuse.

We know an angle to be 23 degrees.

We were also given the side opposite to this angle to be 1200km.

Therefore we use the sine ratio.

6 0

3 years ago

Read 2 more answers

What is $16.50 x 7%

Alexus [3.1K]

Answer:

1.155

Step-by-step explanation:

4 0

3 years ago

I need to know what the answer is?<br>is it x,y,z,or w?

andrew-mc [135]

Answer:

Y

Step-by-step explanation:

5 0

3 years ago

Find the perimeter of the quarter-circle. Give your answer to the nearest whole number.

Bezzdna [24]

Answer:

The perimeter of the quarter-circle is 200 cm.

Step-by-step explanation:

Given that the angle of quarter-circle is 90°. So using Length of Arc formula, you are able to find the length of curve :

$arc = \frac{θ}{360} \times 2 \: \pi \: r$

Let r be radius = 56 cm,

Let θ = 90°

$arc = \frac{90}{360} \times 2 \times\pi \times 56$

$= \frac{1}{4} \times 2 \times \pi \times 56$

$= \frac{1}{2} \times \pi \times 56$

$= 28\pi \: cm$

We have already found the arc. Next we have to add up together to find the perimeter :

$p = 56 + 56 + 28\pi$

$p = 112 + 28\pi$

$p = 200 \: cm \: (3s.f)$

6 0

2 years ago

Read 2 more answers