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3 years ago

A line passes through the points (-4,1) and (-3,3). This line can be modeled by the equation y = mx + b.

Mathematics

1 answer:

docker41 [41]3 years ago

7 0

Answer:

m= 2

b=9

Step-by-step explanation:

-4, 1 -3,3

put it into y2-x2 divided by y1-x1

y2= 3

x2= 1

y1= -3

x1=-4

3-1 divided by -4--3= 2/1 =2x

get one of the points either -4,1 or -3,3

If you use -4,1 -4=x 1=y

put it into y=mx+b and you get 1= -4(2)+b simplify

1=-8+b add 8 to other side b=9

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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

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

4 0

3 years ago

A group of students auditioned for a theater performance and 3/4 of the group less six students made up the cast of 42 students.

LenKa [72]

Answer:

3/4x-6=42

x=64

Step-by-step explanation:

Let the number of students be x hence 3/4 of this number will be 3/4x

Since the number was 42 if they were 3/4x less six, it means minus six hence

3/4x-6=42

Therefore, the equation will be

3/4x-6=42

Solving the equation

3/4 x=42+6=48

3/4x=48

X=62

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4 years ago

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White raven [17]

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maybe SX (d) is more than b and a so

a<b<c or d not sure which
sorry if I didn't help

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3 years ago

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Serga [27]

Umm maybe 59 kilometers

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vladimir2022 [97]

Answer:

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Step-by-step explanation:

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3 years ago