Answer:
Slope is positive for all x, so always increasing
Step-by-step explanation:
Increasing/decreasing depends on the slope of the function, which is f'
f'(x) = 9x² + 18x + 25
If f'(x) > 0 for all x, then his claim is correct (increasing for all x)
If there's even 1 x-value for which f'(x) is not positive, his claim is incorrect
f'(x) is a quadratic function.
9x² + 18x + 25
9(x² + 2x) + 25
9(x² + 2(x)(1) + 1² - 1²) + 25
9(x + 1)² - 9 + 25
9(x + 1)² + 16
Since the minimum value of f' is 16, it's always positive.
Hence, the claim is correct
Answer: From the 60° angle, the flagpole is the opposite side and the shadow is the adjacent side of the triangle.
tangent 60° = opposite/adjacent
so
tan 60° = 20/x
multiply both sides by x and you have
x · tan60° = 20
divide both sides by tan 60° and you have
x = 20/tan60°
x = 11.5 ft.
if this is wrong sorry don’t be mad but if it’s right then hope this helps
Answer:
a) 84π b) 109.2π
Step-by-step explanation:
The formula to find this is v=πr^2h/3
r=d/2. so the radius (r) is 6 because you have to divide the diameter (12) by 2. and the height is 7. so, 6^2=36 and 36x7=252.
252/3=84
and because the question is asking for the EXACT value, you need to just put the pi symbol next to it. Final answer for a is 84π
B) you need to find 30% of 84, which is 25.2 and add it to 84, and you will get 109.2! Final answer is 109.2π.
12
First figure out of it is a arithmetic or geometric sequence, in this case it is a geometric sequence because you have to multiply, not add to find the next number.
Divide one number, I'll pick 324 by the number before it, 108, you get three.
Now divide 36 by 3, you get 12.
To check, multiply 12 by 3, you get 36, multiply that by 3, you get 108, and so on and so forth.
