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spin [16.1K]
3 years ago
14

42÷2 1/3 And 6 2/9÷5 5/6

Mathematics
1 answer:
Solnce55 [7]3 years ago
8 0
The answers are
1. 18
2. 1 1/15
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Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = 1
velikii [3]

Using the shell method, the volume is given exactly by the definite integral,

2\pi\displaystyle\int_0^1x(1+9x^3)\,\mathrm dx

Splitting up the interval [0, 1] into 5 subintervals gives the partition,

[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]

with left and right endpoints, respectively, for the i-th subinterval

\ell_i=\dfrac{i-1}5

r_i=\dfrac i5

where 1\le i\le5. The midpoint of each subinterval is

m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}{10}

Then the Riemann sum approximating the integral above is

2\pi\displaystyle\sum_{i=1}^5m_i(1+9{m_i}^3)\frac{1-0}5

\dfrac{2\pi}5\displaystyle\sum_{i=1}^5\left(\frac{2i-1}{10}+9\left(\frac{2i-1}{10}\right)^4\right)

\dfrac{2\pi}{5\cdot10^4}\displaystyle\sum_{i=1}^5\left(16i^4-32i^3+24i^2+1992i-999\right)=\frac{112,021\pi}{25,000}\approx\boxed{14.08}

(compare to the actual value of the integral of about 14.45)

3 0
3 years ago
The lengths of the sides of a triangle are represented by 3m, 3m and 3m.
Aleks04 [339]
Q1: The perimeter of the triangle is a + b + c and if each side is the same then it's 3a. In this situation we may write it in its simplest form as 9m. Note that 3(3m) is also correct but it's not the simplest form.

Q2: You're correct, the distributive property of 3(3m) can be written as 3 (2m + m).
3 0
3 years ago
Using the formula find the slope of a line with the points (10,20) and (30,50).
VARVARA [1.3K]

Answer:

m = 2/3

Step-by-step explanation:

Slope is defined as the ratio rise/run.

As we move from (10, 20) to (30, 50), the run is 30 - 10, or 20, and the rise is 50 - 20, or 30.  Thus, the slope of the line is m = 30/20, or 2/3.

3 0
3 years ago
Express 0.208 (the 8 is repeating) as a fraction in simplest form.<br><br> 10 POINT AWARD
den301095 [7]
Let x=0.208bar or 0.20888...

1000x=208.888 and 100x=20.888 so

1000x-100x=208.888-20.888

900x=188

x=47/225
5 0
3 years ago
Which of the following is the inverse of y = 3 Superscript x?
Alina [70]

Answer:

- f−1=log3x. Explanation: y=3x ⇒log3y=log3(3x) (logarithms of both side are equal) ⇒x=log3y ⇒f−1=log3x.Step-by-step explanation:

4 0
3 years ago
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