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3 years ago

8

On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the mid

point of AB?
A) -3
B) -2
C) 0
D) 4

1 answer:

damaskus [11]3 years ago

5 0

In my opinion
The answer is B

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1.2%of 45 what is the answer

drek231 [11]

Answer:

0.54

Step-by-step explanation:

1.2/100*45

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3 years ago

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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.

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3 years ago

Mai runs around a 400 meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4

goldfiish [28.3K]

Answer:

6.4 minutes, or 6 minutes and 24 seconds

Step-by-step explanation:

She is running 4 laps, so she is running 1600 meters total. If she runs 250 meters per minute, divide 1600 by 250 to determine how many minutes it will take...

1600/250 = 6.4

Which is 6 minutes + 0.4 minutes

*there are 60 seconds in a minute, so the 0.4 represents 40% of another minute. Multiply 60 by 0.4 to see how many seconds this is...

(0.4)60 = 24 seconds,

So she ran the laps in 6 minutes and 24 seconds

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3 years ago

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Adelle solved the equation, 4x/7 - 6 = -20 , as shown.

Ne4ueva [31]

Answer:

Step 1: Given

Step 2: Add 6 on both sides

Step 3: Multiply 7 on both sides

Step 4: Divide by 4 on both sides

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3 years ago

I'll mark as brainliest if you get the answer correct with Explanation.

mrs_skeptik [129]

Answer:

25, 90, and 65

Step-by-step explanation:

so the measures have to add up to 180, because it's a triangle, and we know 25 and 90 ( the box corner thing means that angle is 90) so we add 25 and 90 to get 115, and then we subtract 115 from 180, which gets us 65.

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3 years ago