Charles is

Mathematics

1 answer:

Alja [10]3 years ago

7 0

Answer:

Charles = 18

Barbara = 3

Step-by-step explanation:

Currently

Charles: x+15

Barbara: x

In twelve years

Charles: x+27

Barbara: x+12

Equation - Charles's age in twelve years will be double Barbara's age in twelve years. Using the information about, create the equation

x+27=2(x+12)

x+27=2x+24

x=3

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Find the greatest common factor of 24, 64, 108.

Ainat [17]

Answer:

The answer is 4.

Step-by-step explanation:

To find the greatest common factor (GCF), start by listing the factors of each number.

For 24: 1, 2, 3, 4, 6, 8, 12, 24

For 64: 1, 2, 4, 8, 16, 32, 64

For 108: 1, 2, 3, 4, 6, 9, 12, 18

Since all the factors are now written out, we can find the greatest common factor between 24, 64, and 108, and the GCF is 4.

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(9x^4-3x^3+4x^2+5x+7) + (11x^4-4x^2-11x-9)

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Answer:

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Darina [25.2K]

Answer:

Given definite integral as a limit of Riemann sums is:

$\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Step-by-step explanation:

Given definite integral is:

$\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}$

Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$