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3 years ago

Peter sells shoes. On Monday he sold 12

Mathematics

1 answer:

rjkz [21]3 years ago

7 0

2 shoes in a hour ....

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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

7. For a school fundraiser, Elena will make T-shirts. She will order T-shirts and print graphics on them. Elena must spend $349

MrRa [10]

Answer: a)

20 shirts | 349 + 20(4.8)

40 shirts | 349 + 40(4.8)

60 shirts | 349 + 60(4.8)

b) Tn = 349 + n(4.8)

c) (1000 - 349)/4.8 rounded down.

7 0

2 years ago

How do you solve this question and what’s the answer

shutvik [7]

Answer:

7.74 square cm

Step-by-step explanation:

To find the leftovers, calculate the area of the square and the area of the circle. Then subtract the two.

Square: A = s*s = 6*6 = 36

Circle: $A = \pi r^2\\A = \pi 3^2\\A = 9 \pi\\A= 28.26$

The area leftover is A = 36 - 28.26 = 7.74

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2 years ago

if layla can right 20 essays in 15 minutes and 8 in 6 minutes then how many can she right in 45 minutes?

scoray [572]

Answer:

60! hope this helps!

Step-by-step explanation:

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2 years ago

What is the slope of the line X=-3?

Mars2501 [29]

Answer:

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Step-by-step explanation:

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2 years ago

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