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3 years ago

La diferencia entre el cuadrado de un número y 8 es igual a 7 veces ese número. Encuentra la solución positiva

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

6 0

Answer:

English?

Step-by-step explanation:

And I prob don't know

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Is 3pi/4pi a rational number?

Natali5045456 [20]

Answer:No

Step-by-step explanation:

Pi is irrational

4 0

3 years ago

Ten members of the academic team went to a local restaurant after their contest. Each meal combo that came with soda cost $6.75,

Aneli [31]

Answer:

7 ordered with Soda;

3 ordered with water

Step-by-step explanation:

Given

$m \to$ With water

$n \to$ With Soda

So:

$m + n =10$ --- total

$5m + 6.75n = 62.25$ -- cost

Required

Find m and n

$m + n =10$

Make m the subject

$m = 10 - n$

Substitute $m = 10 - n$ in $5m + 6.75n = 62.25$

$5(10-n) +6.75n = 62.25$

$50-5n +6.75n = 62.25$

Collect like terms

$-5n +6.75n = 62.25 - 50$

$-5n +6.75n = 12.25$

$1.75n = 12.25$

Solve for n

$n = 12.25/1.75$

$n = 7$

$m = 10 - n$

$m = 10 - 7$

$m =3$

8 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

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

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

What is the value of x

Zolol [24]

Answer:

765854sdfgh

Step-by-step explanation:

6 0

3 years ago

Two friends are reading the same book. Amy can read 3 pages per minute, and she has already read 9 pages. Sam, who has a reading

Daniel [21]

Amy: (3 pages/min)(x min) + 9 pages
Sam: (2 pages/min)(x min) + 47 pages

Equate these: 3x+9 = 2x + 47

Then x = 38. The two friends will have covered the same number of pages after 38 minutes. How many pages would that be? 3(38)+9 = 123 pages.

5 0

4 years ago