Answer: 11 magazines
Step-by-step explanation:
1) 20/5 = $4 per magazine
2) 44/4 = 11 magazines
9 sides
Method 1: Since the interior angle 140 degrees, the supplement of this is the exterior angle and equal to 40 degrees. Hence the number of sides is 360/40 = 9 sides.
When two lines are <em><u>parallel, that means they have the same slope! </u></em>
The slope is the coefficient of x
In the equation y = 3x, <u>the slope is 3 </u>
An example of a line that is above y = 3x is ...
y = 3x + 2
The "+2" <em>shifts the line up </em>by 2 on the y axis
An examples of a line that is below y = 3x is ...
y = 3x - 3
The "-3" <em>shifts the line down</em> by 3 on the y axis
Answer:
The volume of the prism is 1562.4 cm^3.
Step-by-step explanation:
The prism is a geometric figure that has a rectangle on its base and a piramid like top with the shape of a rectangular triangle. It's volume is given by the product of the area of the base by the hight of the triangle. In order to find it we have to perform the following calculations:
V = (area of the base)*h
V = (173.6)*9 = 1562.4 cm^3
It sounds like <em>R</em> is the region (in polar coordinates)
<em>R</em> = {(<em>r</em>, <em>θ</em>) : 2 ≤ <em>r</em> ≤ 3 and 0 ≤ <em>θ</em> ≤ <em>π</em>/2}
Then the integral is
![\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ciint_R%5Cfrac%7B%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%7D%7D%20%3D%20%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_2%5E3%20%5Cfrac%7Br%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%7D%7B%5Csqrt%7Br%5E2%7D%7D%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E%7B%5Cpi%2F2%7D%5Cint_2%5E3%20%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta%20%5C%5C%5C%5C%20%3D%20%5Cfrac%5Cpi2%5Cint_2%5E3%20%5Cmathrm%20dr%20%5C%5C%5C%5C%20%3D%20%5Cfrac%5Cpi2r%5Cbigg%7C_2%5E3%20%3D%20%5Cfrac%5Cpi2%20%283-2%29%20%3D%20%5Cboxed%7B%5Cfrac%5Cpi2%7D)