Answer:
Graph the inequality by finding the boundary line, then shading the appropriate area.
y
<
3
+ x/2
Step-by-step explanation:
Answer:
ok:)))
Step-by-step explanation:
<u>Answer:</u>
![x = 23.6](https://tex.z-dn.net/?f=x%20%3D%2023.6)
<u>Step-by-step explanation:</u>
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is
(required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
.
Substituting into the formula:
![cos (38^{\circ}) = \frac{x}{30}](https://tex.z-dn.net/?f=cos%20%2838%5E%7B%5Ccirc%7D%29%20%3D%20%5Cfrac%7Bx%7D%7B30%7D)
⇒ ![x = cos(38^{\circ}) \times 30](https://tex.z-dn.net/?f=x%20%3D%20cos%2838%5E%7B%5Ccirc%7D%29%20%5Ctimes%2030)
⇒ ![x = 23.6](https://tex.z-dn.net/?f=x%20%3D%2023.6)
![I=\displaystyle\iint_D\mathrm dA=\int_{x=0}^{x=4}\int_{y=0}^{y=4-x}\mathrm dy\,\mathrm dx](https://tex.z-dn.net/?f=I%3D%5Cdisplaystyle%5Ciint_D%5Cmathrm%20dA%3D%5Cint_%7Bx%3D0%7D%5E%7Bx%3D4%7D%5Cint_%7By%3D0%7D%5E%7By%3D4-x%7D%5Cmathrm%20dy%5C%2C%5Cmathrm%20dx)
![I=\displaystyle\int_{x=0}^{x=4}(4-x)\,\mathrm dx](https://tex.z-dn.net/?f=I%3D%5Cdisplaystyle%5Cint_%7Bx%3D0%7D%5E%7Bx%3D4%7D%284-x%29%5C%2C%5Cmathrm%20dx)
![I=8](https://tex.z-dn.net/?f=I%3D8)
To verify this, we can simply find the area of the triangle using the well-known formula
![\dfrac12bh](https://tex.z-dn.net/?f=%5Cdfrac12bh)
, where
![b](https://tex.z-dn.net/?f=b)
and
![h](https://tex.z-dn.net/?f=h)
are the base and height, respectively of the triangular region
![D](https://tex.z-dn.net/?f=D)
. We have
![b=h=4](https://tex.z-dn.net/?f=b%3Dh%3D4)
, so the area is
![\dfrac{4^2}2=8](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5E2%7D2%3D8)
, as expected.