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stepan [7]
2 years ago
5

The nth term is a sequence is 2n-1 the nth term in a different sequence is 3n+1

Mathematics
1 answer:
stepladder [879]2 years ago
5 0

answers

6n² - n - 1

Step-by-step explanation:

2n x 3n +2n - 3n - 1

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Determine whether or not f is a gradient vector field. if it is, find a function φ such that f = ∇φ. (if the vector field is not
MArishka [77]
\mathbf f(x,y)=(2x-6y)\,\mathbf i+(-6x+10y-7)\,\mathbf j

For \mathbf f to be the gradient of some scalar function \varphi(x,y), we need to find \varphi that satisfies

\dfrac{\partial \varphi}{\partial x}=2x-6y
\dfrac{\partial \varphi}{\partial y}=-6x+10y-7

From the first PDE, it follows that (upon integrating with respect to x)

\varphi(x,y)=x^2-6xy+g(y)

Differentiating with respect to y yields

\dfrac{\partial\varphi}{\partial y}=-6x+10y-7=-6x+\dfrac{\mathrm dg}{\mathrm dy}
\implies\dfrac{\mathrm dg}{\mathrm dy}=10y-7\implies g(y)=5y^2-7y+C

\implies\varphi(x,y)=x^2-6xy+5y^2-7y+C
4 0
4 years ago
Sam's age is 2 years less than 3 times Kim's age. If Kim's age is x years, which expression best shows Sam's age?
Nonamiya [84]
Answer is 3x -2
Kim's age is 3 multiply x=3x
since Sam is 2 years less
Sam's age= 3x-2
3 0
3 years ago
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Which equation describe this kine (-2,4), (1,13)
Svetradugi [14.3K]

Slope of the line = (13-4)/(1- -2) = 9/3 = 3


y - y1 = m(x - x1)


y - 4 = 3(x - -2)

y- 4 = 3x + 6


y = 3x + 10 Answer

4 0
3 years ago
Write an equation in point-slope form of the line that passes through the two given points. Use the first point to write the equ
LekaFEV [45]

Answer:

The equation in point-slope form of the line is:

y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)

Step-by-step explanation:

Given the points

  • (-1, -5)
  • (3, 2)

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:2\right)

m=\frac{2-\left(-5\right)}{3-\left(-1\right)}

m=\frac{7}{4}

As the point-slope form is defined as

y-y_1=m\left(x-x_1\right)

where m is the slope.

substituting the values m=7/4 and the first point (-1, -5)

y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)

Therefore, the equation in point-slope form of the line is:

y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)

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3 years ago
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Chegg.com has the answer to this question.
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