A function is created to represent the costs of living per person in the family. What restrictions would be made to the domain?

1 answer:

7 0

The domain would only include positive integers, assuming x is the number of people and y is the dollar amount. You can't have a negative number of people and you also cannot have a fraction of a person.

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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

How do you show work to 4-2+6•2

MatroZZZ [7]

4-2=2
6*2=12

2+12=14

14 is the answer

6 0

2 years ago

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A decimal number changed to 23.7 after it was rounded

lara [203]

The awnser is 24.0 or 24

7 0

2 years ago

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Evaluate for x = 2. (12x + 8) 4 A) 4 B) 5 C) 6 D) 8

Aleks [24]

What you want to do here is plug 2 in for x. when a question asks you to evaluate a certain equation at a certain number, it's just asking you to plug the value in for your variable. i'm assuming that 12x + 8 is meant to be set over 4 as a fraction.

(12(2) + 8)/4 ... figure out the top first. 12*2 = 24, 24 + 8 = 32.

32/4 = 8, so your correct choice is D.

3 0

3 years ago

(5 + 4 - 2) x (-2) = ? A. -22 B. 22 C. 14 D. -15

brilliants [131]

It would actually be -14 because 5+4-2=7 and if you multiply 7 by -2 you get -14

4 0

3 years ago

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