Volume and surface area plz!!!

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

3 years ago

What equation can I make out of this problem

Ghella [55]

5(4)+5x=60
x=8
x= number of pies the club made

7 0

3 years ago

Seventy-eigth hundred-thousandths

s2008m [1.1K]

The decimal number for seventy eight hundred-thousandths is 5.

<h3>What is decimal number?</h3>

A decimal is a number that consists of a whole and a fractional part

The decimal numeral system is the standard system for denoting integer and non-integer numbers.

What is the decimal number for seventy eight hundred-thousandths?

= 78 x 10⁻⁵

<u>note</u>: a hundred thousandth = 10⁻⁵

= 0.00078

Thus, the decimal number for seventy eight hundred-thousandths is 5.

Learn more about decimal number here: brainly.com/question/1827193

#SPJ1

8 0

1 year ago

Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x. M

aev [14]

Answer: d.3,500 + 0.06x > 4,000 + 0.04x

Step-by-step explanation:

Hi, to answer this question we have to write each inequality:

Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x.

So, his monthly earnings must be equal to the sum of the fixed monthly salary ($3500) plus the product of the number of sales (x) and the commission percentage in decimal form (divided by 100):

So:

Jose’s earnings: 3,500 + x (6/100)

Jose’s earnings: 3,500 + 0.06x

Maris earns a monthly salary of $4,000 plus a 4% commission on her sales.

So, her monthly earnings must be equal to the sum of the fixed monthly salary ($4000) plus the product of the number of sales (x) and the commission percentage in decimal form (divided by 100):

Maris’ earnings: 4000+ x (4/100)

Maris’ earnings: 4000+ 0.04 x

Since Jose's earnings must be greater than Maris' earnings

3,500 + 0.06x >4000+ 0.04 x

4 0

3 years ago

Monique worked for 4 hours and earned $39.79. How much would she earn if she worked for 6 hours? I HELP WITH IT RNN

loris [4]

Answer:

x=$59.69

Step-by-step explanation:

We can create a proportion to find the answer.

Thus, we get 4 hr/$39.79=6 hr/$x.

Cross multiplying gives us 4x=238.74, and solving for x gives us $59.685.

We can round to $59.69.

5 0

2 years ago