Let the number of reptiles on endangered list be 'x'
2x + 16=158
2x=158-16
2x=142
x=71
So there are 71 reptiles on the endangered list
Answer:
Since 3 is evenly divided by 9, we can multiply just one term to get a common denominator. Multiply 2 by 3, and get 6, then we multiply 3 by 3 and get 9.
Step-by-step explanation:
9514 1404 393
Answer:
96 yards
Step-by-step explanation:
The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.
The diagonal is the hypotenuse, so we have ...
100² = 28² + w²
w = √(10000 -784) = 96
The width of the park is 96 yards.
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<em>Additional comment</em>
The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).
You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.
<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
