If I had 34 Hershey bars and I ate 2, but I get 69 more and you divide that by 420 what do you get?

The circle below is centered at the origin, and the length of its radius is 7. What is the circle's equation. A. 7x+7y=49. B. x^

Scilla [17]

Equation of a circle is: (x−h)2+(y−k)2=r2 h is the x-coordinate of the center and k is the y-coordinate of the center. Even though the formula has minus signs, those are positive numbers. If there were plus signs in there, the numbers h and k would actually be negative. Now since you're centered at the origin, that means h and k are 0, so you'd just have this: x2+y2=r2 Now since your radius is 7, just square it and replace r^2 woth that value :)

6 0

3 years ago

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As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge o

BartSMP [9]

Let the maximum number of pages Jennifer can have be = x

Amount Jennifer has (P) = $62.10

Given equation is :

P = $(20+0.5x)+0.15(20+0.5x)$

Price is given = 62.10 , so equation is :

$62.10=(20+0.5x)+0.15(20+0.5x)$

$62.10=20+0.5x+3+0.075x$

$62.10=23+0.575x$

$0.575x=39.10$

$x=68$

Hence, Jennifer can have a maximum of 68 pages in her book.

5 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

4x − 30 = ≤12 solve the inequality.

mafiozo [28]

Answer:

4x − 30 = ≤12

Step-by-step explanation:

4x − 30 = ≤12

+30 on both sides

4x≤42

divided by 4 on both sides

x≤10.5

4 0

2 years ago

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PLZ HELP A submarine is exploring the Pacific Ocean. At 502.5 feet below sea level, the water temperature is 63 1/4 °F. The subm

LenaWriter [7]

The submarine is now 617.5 feet below sea level, or at -617.5 feet. the temperature is now at 65 9/20

you have to add the first values with the second values :)

6 0

3 years ago