The triangle inequality states that in a triangle, any two of the side lengths must add up to a length that is greater than the third. That is, if you have a triangle with sides a, b, and c, then a+b>c, a+c>b, and b+c>a.
In this case, we are given two lengths of a triangle. Let's call those two values a and b, where a>b.
Then we have that c
Now we can also use another inequality, a
Now we can apply these limits to all the individual questions.
1) 13 - 10 < c < 13 + 10. This simplifies down to 3 < c < 23
2) 12 - 5 < c < 12 + 5. This simplifies down to 7 < c < 17
3) 11 - 4 < c < 11 + 4. This simplifies down to 7 < c < 15
Hope it help!
The easiest way to find percentages of numbers is to change the percentage to a decimal and multiply it by the number.
30%=0.3
150*0.3=45
30% of 150 is 45.
I hope this helps :)
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
Tangents to a circle from the same point are the same length.
43 -2x = 12x +1
42 = 14x . . . . . . . add 2x-1
3 = x . . . . . . . divide by 14
Answer:
-12
Step-by-step explanation:
-6 - -4*-3/-2
-6 - 12/-2
-6-6
-12
Answer:
a) d²y/dx² = ½ x + y − ½
b) Relative minimum
Step-by-step explanation:
a) Take the derivative with respect to x.
dy/dx = ½ x + y − 1
d²y/dx² = ½ + dy/dx
d²y/dx² = ½ + (½ x + y − 1)
d²y/dx² = ½ x + y − ½
b) At (0, 1), the first and second derivatives are:
dy/dx = ½ (0) + (1) − 1
dy/dx = 0
d²y/dx² = ½ (0) + (1) − ½
d²y/dx² = ½
The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.
