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Softa [21]
3 years ago
9

Define the terms factor and quantity. Then for the expression −3(4+x)(z−2−y), list all of the factors, and specify which are qua

ntities.
Mathematics
1 answer:
omeli [17]3 years ago
4 0

Answer:

A factor are numbers or variables that can be being multiplied to each other to get another number. A factor is a quantity which is used to multiply or divide another quantity to indicate a measurement difference

A quantity is the total number or amount and it is the subject in a given mathematical operation

In the expression, -3×(4 + x)×(z - 2 - y), the factors are;

-3, (4 + x), and (z - 2 - y)

The quantities are the values that are subject to the mathematical operations including;

3, 4, x, z, 2, and y

Step-by-step explanation:

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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,

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

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

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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)

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Step-by-step explanation:

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