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.
Turn each number into the product of it's prime factors.
32=16x2=2x2x2x2x2=2^5
48=24*2=6x4x2=2x3x2x2x2
Pick the highest number that occurs. In this case it is 2. Now we have to see how many times it appears in both. It appears 5 times in 32 and 4 times in 48. 4 is the highest number of times it appears in the numbers so:
2^4=2x2x2x2=16
The Greatest Common Factor (GCF) of 32 and 48 is 16.
The answer to question 3 is D. 15(4a+3). And the answer to question 4 is A. 90. Have a great day
1035.33156649 meters high is the helicopter flying over the building.
Given that, an observer (O) is located 900 feet from a building (B). The observer notices a helicopter (H) flying at a 49° angle of elevation.
We need to find how high is the helicopter flying over the building.
<h3>How to find the height of the building using trigonometry?</h3>
To measure the heights and distances of different objects, we use trigonometric ratios.
Here, use the Tangent rule to calculate the height of the building.
tan(angle) = opposite/adjacent
Now, tan 49°=h/900
⇒h=1035.33156649 meters
Therefore, 1035.33156649 meters high is the helicopter flying over the building.
To learn more about the angle of elevation visit:
brainly.com/question/21137209.
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