Please help i really don't understand
1 answer:
Answer:
80 square units
Step-by-step explanation:
The area formula refers to a generic triangle ABC in which side lengths 'a' and 'b' are known and angle C is between those sides.
In the given figure, we have known side lengths of 12 and 14, and the angle between them is 72°.
Putting these numbers into the formula, we find the area to be ...
A = (1/2)(12)(14)sin(72°) ≈ 79.9 ≈ 80 . . . . square units
The area of the triangle is about 80 square units.
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9514 1404 393
Answer:
a) f(x)
b) g(x)
c) for all values of x > 1, g(x) has a greater rate of change
Step-by-step explanation:
a) The rate of change of f(x) is the x-coefficient: 4. The average rate of change of g(x) on an interval can be found by dividing the change by the interval width. Here, the width of the interval of interest is 1-0 = 1, so the average rate of change is g(1) -g(0) = 4-2 = 2.
On the interval [0, 1], f(x) has the greater rate of change.
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b) The interval [2, 3] also has a width of 1, so the rate of change of g(x) on that interval is g(3) -g(2) = 20 -10 = 10. This value is greater than 4, so ...
on the interval [2, 3], g(x) has the greater rate of change.
__
c) Part (b) demonstrates that g(x) will have a greater rate of change on some intervals. In fact, for any interval whose center is greater than x=1, g(x) will have a greater rate of change than f(x).
_____
In calculus terms, the rate of change of g(x) is g'(x) = 4x. This will be greater than 4 for any x > 1. The graph shows the rate of change is 4 at x=1, and is higher for x > 1. The average rate of change will be greater than 4 on any interval whose center is greater than x=1.
We can figure the average rate of change on the interval [a, b] as ...
m = (g(b) -g(a))/(b -a)
m = ((2b² +2) -(2a² +2))/(b -a) = 2(b² -a²)/(b-a) = 2(b+a)
For the average rate of change to exceed 4, the sum of the ends of the interval must exceed 2, which is to say the midpoint must exceed 1.
I didnt have room for 7 so ill just write it here
20O-12x<60
-12x<-140
X>11.6666..or 11 2/3
20O-12x<60
-12x<-140
X>11.6666..or 11 2/3