Answer:
in 8.6 year will be $4000 be due in order present value $2000
Step-by-step explanation:
given data
P = 4,000 ![e^{-0.08t}](https://tex.z-dn.net/?f=e%5E%7B-0.08t%7D)
amount = $4000
present value = $2000
solution
we consider here present value P and amount A t time at annual nominal year rate r
so
P = A
.................1
so put here P is $2000 and is and A is $4000
2000 = 4000
take ln both side
ln
= ln ![e^{-0.08t}](https://tex.z-dn.net/?f=e%5E%7B-0.08t%7D)
ln2 - ln 4 = -0.08 t
t = 8.664
so in 8.6 year will be $4000 be due in order present value $2000
Just input 45 where the c is.Answer should be 113
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
![=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352]](https://tex.z-dn.net/?f=%3D2%5Cint%5Climits%5E9_4%20%7B%5Cfrac%7B1%7D%7Bu%7D%20%7D%20%5C%2C%20du%5C%5C%5C%5C%20%3D%202%5B%28log~u%29%5D_4%5E%7B9%7D%5C%5C%5C%5C%3D2%5B%28log~9-log~4%29%5D%5C%5C%5C%5C%3D2%5Ctimes%5B0.352%5D)
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
Learn more about the average density here:
brainly.com/question/15118421
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Answer:
I think the second one is not an equation
(but I'm not sure)
hope this helped
By applying definition of limits, the <em>end</em> behavior of the <em>rational</em> function f(x) = 10/(x² - 7 · x - 30) is represented for the <em>horizontal</em> asymptote x = 0.
<h3>What is the end behavior of a rational function</h3>
The <em>end</em> behavior of a <em>rational</em> functions is the horizontal asymptote of the <em>rational</em> function when x tends to ± ∞. Then, we find the end behavior by applying limits:
![\lim_{x \to \pm \infty} \frac{10}{x^{2}-7\cdot x - 30}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%5Cfrac%7B10%7D%7Bx%5E%7B2%7D-7%5Ccdot%20x%20-%2030%7D)
![\lim_{n \to \infty} \frac{10}{x^{2}-7\cdot x - 30}\cdot \frac{x^{2}}{x^{2}}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B10%7D%7Bx%5E%7B2%7D-7%5Ccdot%20x%20-%2030%7D%5Ccdot%20%5Cfrac%7Bx%5E%7B2%7D%7D%7Bx%5E%7B2%7D%7D)
![\lim_{x \to \pm \infty} \frac{\frac{10}{x^{2}} }{1 - \frac{7}{x}-\frac{30}{x^{2}}}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%20%5Cfrac%7B%5Cfrac%7B10%7D%7Bx%5E%7B2%7D%7D%20%7D%7B1%20-%20%5Cfrac%7B7%7D%7Bx%7D-%5Cfrac%7B30%7D%7Bx%5E%7B2%7D%7D%7D)
![\lim_{x \to \pm \infty} 0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cpm%20%5Cinfty%7D%200)
0
By applying definition of limits, the <em>end</em> behavior of the <em>rational</em> function f(x) = 10/(x² - 7 · x - 30) is represented for the <em>horizontal</em> asymptote x = 0.
To learn more on end behavior: brainly.com/question/27514660
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