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3 years ago

The equation of a line is y=-2x+1. What is the equation of a line that is parallel to the first line and passes through (2,2)

Mathematics

1 answer:

Alex3 years ago

7 0

The answer is y=-2x+6

We know the slope of the given equation is -2. A parallel line must have the same slope as the original function. So if we plug in the coordinates and the slope into the point slope formula we get y=-2x +6

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<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%20%5Cinfty%20%20%5Cfrac%7B%20%5Csqrt%5B%20%20%5Cscriptsize%5Cphi%

Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

$I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx$

Replace $x \to x^{\frac1\phi} = x^{\phi-1}$ :

$I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

Split the integral at x = 1. For the integral over [1, ∞), substitute $x \to \frac1x$ :

$\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

The integrals involving tan⁻¹ disappear, and we're left with

$I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}$

8 0

2 years ago

.004 greater than or less than 4.00

Goshia [24]

Answer:

0.004 is much less than 4.00!

4 0

3 years ago

Read 2 more answers

7. Find the slope of the line.

svetoff [14.1K]

Answer:

1/5

Explanation:

For every two minutes, 10 items get sold. 2/10 is equivalent to 1/5

4 0

2 years ago

Read 2 more answers

Kim was walking down a rocky path.For 4 minutes, the elevation dropped steadily.All together it dropped 8 feet. What was the cha

fenix001 [56]

Answer:

2 $\frac {{\textrm{feet}}}{{\textrm{minute}}}$

Step-by-step explanation:

Kim was walking down a rocky path. For 4 minutes, the elevation dropped steadily. All together it dropped 8 feet.

So, the change in elevation per minute for the 4 minutes is given by,

$\frac {8}{4} \frac {{\textrm{feet}}}{{\textrm{minute}}}$

= 2 $\frac {{\textrm{feet}}}{{\textrm{minute}}}$

(Answer)

8 0

3 years ago

Which binomial is a factor of49x^2+84xy+36y^2

Alex17521 [72]

Answer:

(7 x + 6 y)^2

Step-by-step explanation:

Factor the following:

49 x^2 + 84 x y + 36 y^2

The coefficient of x^2 is 49 and the coefficient of y^2 is 36. The product of 49 and 36 is 1764. The factors of 1764 which sum to 84 are 42 and 42. So 49 x^2 + 84 x y + 36 y^2 = 49 x^2 + 42 x y + 42 x y + 36 y^2 = 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

7 x (7 x + 6 y) + 6 y (7 x + 6 y)

Factor 7 x + 6 y from 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

(7 x + 6 y) (7 x + 6 y)

(7 x + 6 y) (7 x + 6 y) = (7 x + 6 y)^2:

Answer: (7 x + 6 y)^2

3 0

3 years ago