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2 years ago

How many solutions does this system have? y = 3/4x - 5. - 3 x + 4 y = - 20.

Mathematics

1 answer:

dedylja [7]2 years ago

4 0

Answer:

infinite

Step-by-step explanation:

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Use a graphing calculator or online application to find the solutions to x 2 - 9 = to the nearest tenth. The solution is approxi

drek231 [11]

X^2-9=0 add 9 to both sides

x^2=9 take the square root of both sides

x=±3

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3 years ago

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Evaluate the expression 9

Sindrei [870]

Answer:

Step-by-step explanation:

9/3

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2 years ago

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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

–6 + (–12)<br><br><br>Evaluate the expression

Elanso [62]

Answer:

-18.

Step-by-step explanation:

They're both negative numbers being added to each other, so you'd add 6 and 12 (which is 18) and then put a negative sign before the 18. Therefore, your answer is -18.

I hope this helps, have a nice day.

3 0

2 years ago

Wilbur runs 3.2 km every morning how many feet are in 3.2 km given that 1 mile = 1.609 km and 1 mile = 5,280

Nonamiya [84]

1.609/5280 = 3.2/x....1.609 km to 5380 ft = 3.2 km to x ft
cross multiply because this is a proportion
(1.609)(x) = (5280)(3.2)
1.609x = 16896
x = 16896/1.609
x = 10,500 ft <===

5 0

3 years ago

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