Answer and Step-by-step explanation:
Let x and y be two positive integers and their sum is 14:
X + y = 14
And the sum of square of this number is:
f = x2 + y2
= x2+ (14 – x)2
Differentiate with respect to x, we get:
F’(x) = [ x2 + (14 – x)2]’ = 0
2x + 2(14-x)(-1) = 0
2x +( 28 – 2x)(-1) = 0
2x – 28 +2x = 0
2x + 2x = 28
4x = 28
X = 7
Hence, y = 14 – x = 14 -7 = 7
Now taking second derivative test:
F”(x) > 0
For x = y = 7,f reaches its maximum value:
(7)2 + (7)2 = 49 + 49
= 98
F at endpoints x Є [ 0, 14]
F(0) = 02 + (14 – 0)2
= 196
F(14) = (14)2 + (14 – 14)2
= 196
Hence the sum of squares of these numbers is minimum when x = y = 7
And maximum when numbers are 0 and 14.
If c = 8 and d = -5:
a) c - 3 = 8 - 3
= 5
b) 15 - c = 15 - 8
= 7
c) 3(c + d) = 3(8 + (-5))
= 3*3
= 9
d) 2c - 4d = 2(8) - 4(-5)
= 16 + 20
= 36
e) d - c^2 = -5 - (8)^2
= -5 - 64
= -69
f) 2d^2 + 5d = 2(-5)^2 + 5(-5)
= 50 - 25
= 25
Hey there! I'm happy to help!
You ran a 10 kilometer race in 56 minutes (good job!). To find how much you ran in 1 minute, you simply divide by 56.
10/56=0.178571428
Therefore, you ran around 0.18 km/minute.
Have a wonderful day! :D
We can use vertical opposite angles. Which means the opposite angles where 2 lines intersects is the same.
3x + 50 = 6x - 10 (vert. Opp. Angles)
3x = 6x - 60
-3x = - 60
X = 20°
Answer:
3.42
Step-by-step explanation:
41/12 is 3.42
