Compute: 3^(log3 16) - 5^(log5 11)

Mathematics

1 answer:

Nataliya [291]2 years ago

3 0

Answer:

I feel bad for you

Step-by-step explanation:

sorry.....

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6

Anettt [7]

Splitting up the interval [0, 6] into 6 subintervals means we have

$[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]$

and the respective midpoints are $\dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2$ . We can write these sequentially as ${x_i}^*=\dfrac{2i+1}2$ where $0\le i\le5$ .

So the integral is approximately

$\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2$

Recall that

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$
$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$
$\displaystyle\sum_{i=1}^n1=n$

so our sum becomes

$\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)$
$=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2$

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2 years ago

you own a house cleaning business. it takes you 2 hours and 45 minutes to clean a house. you have 3 houses to clean tomorrow. ho

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3 years ago

3 times 5 with a two on the top

jenyasd209 [6]

Ok so it could be
1. $\frac{2}{3 times 5}$
2. 3 timies $\frac{2}{5}$

ok if 1. then
$\frac{2}{3 times 5}$ = $\frac{2}{15}$

if 2. 3 timies $\frac{2}{5}$ = $\frac{6}{5}$

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