The answers will be:
- (4, 5)
- remain constant and increase
- g(x) exceeds the value of f(x)
<h3>What is Slope and curve?</h3>
a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).
b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).
c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:
f(8) = 4·8 +3 = 35
g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35
g(8) > f(8)
d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).
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Answer:
20%/100 = 8 peeps / 40 items in the basket
(40 total items)
Step-by-step explanation:
Let x be the total number of items in the basket. The ratio of peeps to the total item is 1/5. Therefore,
1/5 = 8/x
x = 40
40 total items
Answer:
6 hours
Step-by-step explanation:
Suppose Madison spent x hours on her social project,
then the number of hours spent on other project will be 1/3 of x=x/3
Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e
x + x/3 = 4x/3
It si given that this is 8 hours, therefore
4x/3=8
Multiplying both sides by 3:
4x=24
Dividing across board by 4:
x= 6 hours
Answer:
85.9 m
Step-by-step explanation:
The law of sines can help figure this.
The remaining angle in the triangle is ...
180° -75° -68° = 37°
This is the angle opposite the leg from the surveyor to the second marker. Referencing the attachment, we have ...
b/sin(B) = c/sin(C)
b = sin(B)·c/sin(C) = 132.3·sin(37°)/sin(68°) ≈ 85.873 . . . meters
The surveyor is about 85.9 meters from the second marker.
