Answer:
The lateral area = 450 mm²
Step-by-step explanation:
The lateral area of any prism is equal to the areas of the sides faces
∵ The base of the prism is triangle
∴ It has 3 side faces
∵ The lengths of the side faces are 5 , 12 , 13 and their height is 15
∴ The lateral area = (5 × 15) + (12 × 15) + (13 × 15)
= 75 + 180 + 195 = 450 mm²
Answer:
82 is 42 degrees warmer than 40
Step-by-step explanation:
if you subtract 40 from 82, you get 42 meaning that the answer will be 42 degrees more than 40
Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Suppose that a>b>1, then
and 
Therefore, since 2<3<7, 
Choose an arbitrary x>1. You have that a takes the greatest values at x, c takes the smallest value at x. Thus,
a>b>c and
Answer: correct option is B.
