Answer with explanation:
Let us assume that the 2 functions are:
1) f(x)
2) g(x)
Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that
Now the sum of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus
Thus the sum of the 2 functions is also a concave function.
Part 2)
The product of the 2 functions is shown below
Diffrentiating both sides with respect to 'x' we get
Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.
Answer:
Step-by-step explanation:
6/5
= 1 1/5
Answer: he can pay for 6 people total (including him)
Step-by-step explanation:
first lets subtract the flat fee from the total amount of money he has
70 - 40 = 30
now lets divide 30 by $4.50 to see how many people he can pay for
30 / $4.50 = about 6.5
obviously you cant pay for half a person so he can invite 5 people (he also has to pay for himself)
The values of the equation will be:
9. 12x - 1
10. -50 - x
11. -x + 14
12. x³ - 4y - 4
13. 8 - 6x
14. 288 - 1080x
15. 420 - y
16. 66 + 7y - 9x
<h3>How to compute the equation?</h3>
9. 4(3x+ 2) - 9
12x + 8 - 9
12x - 1
10. √144 – (62 –x)
12 - (62 - x)
-50 - x
11. (28 ÷ 4) – (x + 7)
7 - x + 7
= -x + 14
12. x³ – 4y - (6 + 2)
x³ - 4y - 4
13. 64 ÷ 8) – (x • 6)
= 8 - 6x
14. 72 (4 - 15x)
288 - 1080x
15. 4(√144 + 93)–y
4(12 + 93) - y
= 420 - y
16. 54 + 7y – (8 + 9x)
= 66 + 7y - 9x
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Answer:
197 in ^2 (answer B of the list)
Step-by-step explanation:
Notice that this figure has a total of 6 faces, four of which are rectangles (whose area is calculated as "base times height") and two trapezoids (whose area is (B+b)H/2 ).
The total surface area is therefore the addition of these six areas:
Rectangles:
5 in x 5 in = 25 in^2
5 in x 5 in = 25 in^2
5 in x 6.4 in = 32 in^2
9 in x 5 in = 45 in^2
Trapezoids:
Two of equal dimensions: B = 9 in, b = 5 in, H = 5 in
2 * (9 in + 5 in) 5 in /2 = 70 in^2
Which gives a total of (25 + 25 + 32+45 + 70) in^2 = 197 in^2
This agrees with answer B of he provided list.