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2 years ago

Please help me solve this I will give u brainlst :)

Mathematics

1 answer:

NARA [144]2 years ago

7 0

Equation: 2(.25) + p(.75) = 2.75
Answer: 3 pencils

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Write 420 as a product 9f prime numbers

stich3 [128]

Answer:

2, 2, 3, 5, 7 that is the farthest you can go

Step-by-step explanation:

2,2,3,5,7 prime factorization of 420 but impossible to get 9 factors

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

2 years ago

NEED HELP!!!<br> WITH PROBLEM

pantera1 [17]

Answer:

x=32 hope it helps, if it does can i get 5.0 or brainliest

Step-by-step explanation:

7 0

2 years ago

Diegos uncle sells computers. In addition to his wages, he gets paid 20% of the amount he sells

Ivahew [28]

Answer:

Answer:

Diego's uncle earned $600 because he told $3000 worth of computers.

Step-by-step explanation:

100% divided by 20% = 5

$600 x 5 = $3000

I hope this helps!

Step-by-step explanation:

4 0

2 years ago

Is there an ordered pair solutions to <br> -3x+3y=4 and <br> -x+y=3 ????

elixir [45]

Y=x+3
-3x+3(x+3)=4
-3x+3x+9=4
9=4
Since this statement is false, there are no ordered pair solutions to this problem.

8 0

2 years ago