Simplify this expression (15+8d)(-5)-24d+d Solve step by step

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

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

4 0

3 years ago

The following playing cards are used in a game. What is the probability of not selecting a prime number?

dybincka [34]

Answer:

3/7

Step-by-step explanation:

1,2,3,4,5,6,7

The word problem is asking the PROBABILITY OF NOT SELECTING A PRIME NUMBER.

PROBABILITY: THE LIKELIHOOD OF AN EVENT.

There are 7 numbers in this data set. Of the seven numbers, four are prime numbers, three of them are not.

Therefore, the probability of not selecting a prime number is 3 in 7, or 3 out of 7 (3/7).

3 0

3 years ago

Solve the following system of equations by using the inverse of a matrix.

Zepler [3.9K]

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

6 0

4 years ago

Which of the following scale factors will result in an enlargement? A. k < –1 B. –1 < k < 0 C. 0 < k < 1 D. k = 1

grin007 [14]

Answer:

Option A (k < -1).

Step-by-step explanation:

Enlargement is one of the linear transformations which changes the size of the shape formed by a combination of some points in the exact proportion. For enlargement (also called dilation), there are two parameters required: the center of enlargement, according to which the transformation occurs, and the scale factor, the size by which the transformation is done. The scale factor can be of any number k. If k is larger than 1 or -1, then it will cause enlargement. If k is between -1 and 1, it will cause anti-enlargement. The magnitude of k determines the size and the sign of k determines the direction. So in this case, k < -1 will cause the enlargement: even though the scale factor is less than -1, but it will enlarge the shape on the opposite direction. Option B and Option C cause anti-enlargement and Option D cause no enlargement or anti-enlargement. So Option A is the correct answer!!!

8 0

4 years ago

Read 2 more answers

30 points With explanation plz?

rosijanka [135]

Answer:

girl. . I wanna say 80 but don't count on my answer. hopefully I helped

5 0

4 years ago