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3 years ago

Determine the constant of varlation for the direct variation glven. Rvaries directly with S. When S is 16, R Is 80.

Mathematics

1 answer:

navik [9.2K]3 years ago

4 0

Answer:

The constant of variation is 5.

Step-by-step explanation:

In direct variation, as y varies directly with x, the standard equation is

y = kx,

where k is the constant of variation.

In your case, we use R and S. R varies directly with S, so we have

R = kS

We know that when S = 16, R is 80, so we plug in those values and solve for k, the constant of variation.

R = kS

80 = k(16)

k = 80/16

k = 5

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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

The area of a rectangle is expressed as x4 − 16y^4, determine & state the length and the width of the rectangle, expre

Bad White [126]

Answer:

Step-by-step explanation:

16 = 2 *2 * 2 * 2 = 2⁴

16y⁴ = (2y)⁴

x⁴ - 16y⁴ = x⁴ - (2y)⁴

= (x²)² - [ (2y)² ]²

{Use identity = a² -b² =(a +b)(a- b). Here a =x² & b =(2y)²}

= (x² + (2y)² ) (x² - (2y)² )

= (x² + 4y²) (x² - 4y²)

7 0

3 years ago

If you have the circumference of a circle. How do you find the radius?

algol13

The formula for finding c...” No, you would divide it. The formula for finding circumference is 2 x pi x r, where r is the radius. 2 x r = d, where d is diameter.

6 0

3 years ago

Which size can of green beans shown in the table has the lowest unit price?

posledela

The can of green beans that has the lowest unit price is the 8 oz. size.

To find the unit price of each size, divide the cost by the size. (A number below that's in parentheses means it goes on forever)

0.89 ÷ 6 = 0.148(3)
1.04 ÷ 8 = 0.13
1.69 ÷ 10 = 0.169
4.79 ÷ 32 = 1496875
Among all of these answers, the can with 8 oz. has the least unit price/rate. Thus, this is the answer.

3 0

2 years ago

Estimate the answear by rounding each number to its greatest place: 199 x 91

Nataly [62]

I estimated the answer to be 18,000

Without estimation the answer would be 18,109

3 0

3 years ago

Read 2 more answers

Determine the constant of varlation for the direct variation glven. Rvaries directly with S. When S is 16, R Is 80.​

Determine the constant of varlation for the direct variation glven. Rvaries directly with S. When S is 16, R Is 80.