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3 years ago

What is the equation for the line?

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

HOW TO:
* use slope intercept form

1) find the slope

slope = rise/run (rise divided by the run)
slope = -4/2
slope = -2

2) find the y-intercept (just the point where the line intersects the y-axis)

y-intercept is (0,-4)

3) use slope-intercept form:
y = mx + b (m stands for the slope, b stands for the y-intercept)
y= -2x + (-4)
y= -2x - 4

So your equation is y= -2x-4

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Two numbers have a difference of 8 what is the minimum product of these numbers

Nady [450]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

Juanita has a strip of paper divided into 8 equal sections. She colored 3 of the sections yellow, 2 of the sections black, and t

Musya8 [376]

I think its 2/8 but I'm not sure

5 0

3 years ago

Need help pls and thank you

Mkey [24]

Answer:

y=25x

Step-by-step explanation:

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5 0

2 years ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8$

$r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

3 0

3 years ago

Four times two less than a number is the same as thrice one more than the number. Find the number.

IgorLugansk [536]

Answer:

See below:

Step-by-step explanation:

We can first setup an equation by doing the following:

$4(2-x) = 3(x+1)\\8-4x=3x+3\\8-7x=3\\-7x=3-8\\-7x=-5\\x=-5/-7 (5/7)$

Whole proccess above!

If you would like an explanation, please let me know so.

Its basically algebra and it's mainly on how you interpret it!

Have a nice day!

5 0

2 years ago