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Harlamova29_29 [7]

3 years ago

7

Nathan is buying a cell phone for his business. The regular price for the cell phone is $179. If he buys the phone in the next 2

weeks he gets a 20% discount. What will be the sale price if he buys the phone tomorrow.

1 answer:

stira [4]3 years ago

5 0

He will spend 143.20 dollars

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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

1 year ago

Can someone write the point slope equation

valentinak56 [21]

Since you have the slope, you can start your equation with y= -8/7x +b. To find b, plug the X value for the point you were given in for the X (-8/7•4) you get -32/7 or -4.57. Then you take the given Y value(4) and subtract the number you just found (4-(-4.57)). You get 8.57. That means your equation is Y= -8/7 + 8.57

6 0

3 years ago

A restaurant uses 290 pounds of onions every 2 and a half weeks. If they continue to use onions at the same rate, how many pound

Archy [21]

290/2.5 = 116 pounds per week

116 * 6 = 696 pounds

4 0

2 years ago

Read 2 more answers

What is the answer for 14g > 56?

gulaghasi [49]

G > 4

i hope this helps

4 0

2 years ago

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Fred Salmon purchased six $1,000 bonds at 92. The bonds pay 6.5%, what is the cost of the bonds

soldi70 [24.7K]

The cost of the bond
6×1,000×0.92=5,520

4 0

2 years ago

Read 2 more answers