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bezimeni [28]
3 years ago
12

If Patrick was pushing directly downward on the rock with a force of 10 N. How much work did Patrick do? Show/explain your work.

Mathematics
1 answer:
stiks02 [169]3 years ago
4 0

Answer:

Patrick from spongebob? He dosent do work

Step-by-step explanation:

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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
Which number or numbers have 2 lines of symm
Molodets [167]
5,13,15 and  more!
hope that helps!!!!

5 0
3 years ago
Factor the following expression.<br> x2 + 4x - 5
sashaice [31]

Answer:(x+5)(x-1)

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
ASAP I NEED HELP
alexdok [17]

The vertex of this parabola is at (3,-2). When the x-value is 4, the y-value is 3: (4,3) is a point on the parabola. Let's use the standard equation of a parabola in vertex form:

y-k = a(x-h)^2, where (h,k) is the vertex (here (3,-2)) and (x,y): (4,3) is another point on the parabola. Since (3,-2) is the lowest point of the parabola, and (4,3) is thus higher up, we know that the parabola opens up.

Substituting the given info into the equation y-k = a(x-h)^2, we get:

3-[-2] = a(4-3)^2, or 5 = a(1)^2. Thus, a = 5, and the equation of the parabola is

y+2 = 5(x-3)^2 The coefficient of the x^2 term is thus 5.

7 0
3 years ago
Find the distance between (6,2) and (9,12)
bazaltina [42]
Distance bweteen (x1,y1) and (x2,y2) is
D= \sqrt{(x2-x1)^2+(y2-y1)^2}

so disatnce between (6,2) and (9,12) is
D= \sqrt{(9-6)^2+(12-2)^2}
D= \sqrt{(3)^2+(10)^2}
D= \sqrt{9+100}
D= \sqrt{109}

the distance is√109 units
8 0
3 years ago
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