Which equation matches the statement below?

Mathematics

1 answer:

kvasek [131]1 year ago

8 0

Answer:

3(n-5)=2n+16

Step-by-step explanation:

3 lots of 'n' and 5 means 3 times both values so these values are put into a bracket with a common multiplier (ie. the 3)

3(5 - n)

16 more than 2 lots of 'n' means that n has to be doubled. n + n = 2n. add 16 to this and we have

2n + 16

if these values are both equal (hence why they are in an equation) then all that is needed is for them to be set equal alongside each other.

3(n-5) = 2n+16

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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

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

8 0

2 years ago

A bird (B) is spotted flying 6,000 feet from a tower (T)). An observer (O) spots the top of the tower (T) at a distance of 9,000

Nina [5.8K]

Answer:

The angle will be "48.7°".

Step-by-step explanation:

In ΔTBO, the given values are:

TB = 6,000 feet

BO = 9,000 feet

Now,

To find the angle,