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3 years ago

What is the answer to 3p^4 times 5p^2

Mathematics

1 answer:

sladkih [1.3K]3 years ago

4 0

Answer:

I'm pretty sure the answer is 15p^8

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Ricky has 3/4 of a bag of Skittles. He wants to split the rest between between his 5 friends. What fraction of the bag will each

Wittaler [7]

Answer:

3/20, with the assumptions below.

Explanation:

The question seems incomplete.

In order to show you the procedure, I make some assumptions.

Assuming that Ricky wants to split the full content of the 3/4 of a bag between his 5 friends, to find what fraction of the bag will each friend receive you must divide 3/4 by 5.

The operation is:

$\dfrac{3}{4}\div 5$

Convert the whole number 5 into fraction using 1 as denominator:

$\dfrac{3}{4}\div \dfrac{5}{1}$

Transform the division into multiplication changing the divisor into its reciprocal:

$\dfrac{3}{4}\times \dfrac{1}{5}$

Multiply numerator with numerator and denominator with denominator:

$\dfrac{3\times 1}{4\times 5}=\dfrac{3}{20}\leftarrow answer$

7 0

3 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

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