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2 years ago

Name the postulate or theorem you can use to prove NPM=OMP

Mathematics

1 answer:

Katarina [22]2 years ago

4 0

Answer:

ΔNPM and ΔOMP by SAS postulate

B is correct

Step-by-step explanation:

In ΔNPM and ΔOMP

NP = OM (Given)

∠NPM = ∠OMP (Given)

PM = MP ( Common )

So, ΔNPM ≅ ΔOMP by SAS property of concurrency.

ΔNPM and ΔOMP are congruent because their two side and angle between them are equal.

Therefore, SAS postulate use here

Hence, ΔNPM and ΔOMP by SAS postulate

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Which of the following could identify the transformation of a parabola with a vertex (-4,-6) to parabola with a vertex (1,-6)?

choli [55]

Hello,

2 possibilties:
1) a translation to the right of 5 (both parabolas are turning upward)
2) a central symetry( center is (-1.5,-6)
parabolas does not have the same direction upward and downward.

3 0

2 years ago

Of the 50 U.S. states, 4have names that start with the letter W . What percentage of U.S. states have names that start with the

Verizon [17]

8% of US states start with W

4 0

2 years ago

The measure of angle R is 148° and the measure of angle S is 85°, find the measure of angle T.

Talja [164]

so you have a 148+85+85=318, 360-318=42 is the measure of angle T because all four angles together make 360

8 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

2 years ago

A density curve of all the possible ages between 0 years and 25 years is in the shape of a triangle. What is the height of the t

Bad White [126]

Answer:

Step-by-step explanation:

Note that the area under a probability density curve must be 1.

The formula for the area of a triangle is A = (1/2)(base)(height).

Here the base is 25 units. Thus, A = 1 unit^2 = (1/2)(25 units)(height), or, after multiplying both sides of this equation by 2:

2 units^2 = ( 25 units)(height)

2 units^2

Then (height) = --------------------- = 0.08 unit

25 units

The height of the triangle is 0.08 unit.

3 0

3 years ago