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2 years ago

Evaluate the following fractions giving your awnser in its simplist form. 50 POINTS!

Mathematics

1 answer:

harina [27]2 years ago

6 0

a. 1/ 15

b. 76/ 15

c. 1/12

<h3>How to determine the value</h3>

a. 2/5 divided by 6

= 2/ 5 ÷ 6

= 2/ 5 ÷ 6/ 1

Take the inverse of the dividing fraction, we have

= 2/ 5 × 1/ 6

Multiply through

= 2/30

= 1/ 15

b. 3 and 1/3 times 5 and 2/5

= 3 + 1/ 3 × 5 + 2/ 5

From the knowledge of BODMAS, we multiply first

= 3 + 5/3 + 2/ 5

Find the LCM

= 45 + 25 + 6/ 15

= 76/15

c. 1/4 + 1/3 -1/2

Let's find the LCM

= 3 + 4 - 6 / 12

Add first

= 7 - 6/ 12

= 1/ 12

Learn more about BODMAS here:

brainly.com/question/723406

#SPJ1

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Apply Gaussian quadrature with n = 4 to approximate integrate sin x^2dx from 1 to 5

maks197457 [2]

First, recall that Gaussian quadrature is based around integrating a function over the interval [-1,1], so transform the function argument accordingly to change the integral over [1,5] to an equivalent one over [-1,1].

$x=2t+3\iff t=\dfrac x2-\dfrac32\implies2\mathrm dt=\mathrm dx$
$x=1\implies t=\dfrac{2-6}4=-1$
$x=5\implies t=\dfrac{10-6}4=1$

So,

$\displaystyle\int_{x=1}^{x=5}\sin x^2\,\mathrm dx=\displaystyle2\int_{t=-1}^{t=1}\sin(2t+3)^2\,\mathrm dt$

Let $f(t)=2\sin(2t+3)^2$ . With $n=4$ , we're looking for coefficients $c_i$ and nodes $x_i$ , with $1\le i\le4$ , such that

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx c_1f(x_1)+\cdots+c_4f(x_4)$

You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).

Using the quadrature, we then have

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.3749f(-0.8611)+0.6521f(-0.3400)+0.6521f(0.3400)+0.3749f-0.8611)$
$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.5790$