In the figure below, one side of the right triangle is a diameter of the semicircle.
1 answer:
Answer:
Option (A)
Step-by-step explanation:
One side of the given triangle is a diameter of the semicircle given.
Measure of the diameter = 10 units
Total area of the semicircle =
=
= 39.27 square units
Area of the right triangle =
=
= 24 square units
Area of the shaded region = Area of the semicircle - Area of the right triangle
= 39.27 - 24
= 15.27 square units
≈ 15 square units
Therefore, option (A) will be the answer.
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First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is 
. Set the derivative equal to 0 and factor to find the critical numbers. 
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.
Answer:
Quesnel Lake:Lake Baikal=.31
Quesnel Lake:Great Slave Lake=.82
Step-by-step explanation:
1 foot = .3048 meters
Lake Baikal: 5369 ft. = 1636.4712 m
Great Slave Lake: 2015 ft. = 614.172 m
Quesnel Lake: 506 m
Quesnel Lake:Lake Baikal
Quesnel Lake:Great Slave Lake