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2 years ago

This needs to be done quickly!!

Mathematics

1 answer:

faltersainse [42]2 years ago

6 0

Answer:

3x-5

Step-by-step explanation:

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Danny brought a car for £10000 the value of the car depreciated by 20% in the first year then the value of the car depreciated b

Levart [38]

£7200

In first year depreciates by 20%, that is it is worth 80% of it's original value

80% = $\frac{80}{100}$ = 0.8

value after 1 year = 0.8 × £10000 = £8000

In the second year it depreciates by 10% of it's value, that is it is worth 90% of it's value at the end of the first year.

90% = $\frac{90}{100}$ = 0.9

value after 2 years = 0.9 × £8000 = £7200

6 0

3 years ago

Test the series for convergence or divergence (using ratio test)

Triss [41]

Answer:

$\lim_{n \to \infty} U_n =0$

Given series is convergence by using Leibnitz's rule

Step-by-step explanation:

Step(i):-

Given series is an alternating series

∑ $(-1)^{n} \frac{n^{2} }{n^{3}+3 }$

Let $U_{n} = (-1)^{n} \frac{n^{2} }{n^{3}+3 }$

By using Leibnitz's rule

$U_{n} - U_{n-1} = \frac{n^{2} }{n^{3} +3} - \frac{(n-1)^{2} }{(n-1)^{3}+3 }$

$U_{n} - U_{n-1} = \frac{n^{2}(n-1)^{3} +3)-(n-1)^{2} (n^{3} +3) }{(n^{3} +3)(n-1)^{3} +3)}$

Uₙ-Uₙ₋₁ <0

Step(ii):-

$\lim_{n \to \infty} U_n = \lim_{n \to \infty}\frac{n^{2} }{n^{3}+3 }$

$= \lim_{n \to \infty}\frac{n^{2} }{n^{3}(1+\frac{3}{n^{3} } ) }$

= $= \lim_{n \to \infty}\frac{1 }{n(1+\frac{3}{n^{3} } ) }$

$=\frac{1}{infinite }$

$\lim_{n \to \infty} U_n =0$

∴ Given series is converges

3 0

3 years ago

What can the intersection of a regular octagon and line segment be?

noname [10]

Answer:

See below

Step-by-step explanation:

Intersection of a regular octagon and a line segment can result in:

Triangle (ABC as example)
Quadrilateral (ABCD as example)
Pentagon (ABCDE as example)
Hexagon (ABCDEF as example)
Heptagon (ABCDEFG as example)

Refer to attached

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cint%20%5Cfrac%7Bdx%7D%7Bxln%5E%7Bp%7Dx%20%7D" id="TexFormula1" title=" \int \frac{dx}{xl

Eva8 [605]

Substitute $u=\ln x$ , so that $\mathrm du=\dfrac{\mathrm dx}x$ . The integral is then equivalent to

$\displaystyle\int\frac{\mathrm dx}{x\ln^px}=\int\frac{\mathrm du}{u^p}=\begin{cases}\dfrac{u^{p+1}}{p+1}+C&\text{for }p\neq1\\\\\ln|u|+C&\text{for }p=1\end{cases}$

Then transforming back to $x$ gives

$\displaystyle\int\frac{\mathrm dx}{x\ln^px}=\begin{cases}\dfrac{\ln^{p+1}x}{p+1}+C&\text{for }p\neq1\\\\\ln|\ln x|+C&\text{for }p=1\end{cases}$

4 0

3 years ago

MAKING BRAINLIEST!!Bruce Wayne splits his budget by using the ratio 12:7. For every $12 he spends

Anvisha [2.4K]

D. 28

this is because 48 divided by 12 is 4, 4 times 7 is 28.

3 0

2 years ago

Read 2 more answers