Answer:
A. -2sin(x)sin(0.4x)
Step-by-step explanation:
At x=0, the given expression evaluates to zero.
For x near zero, the given expression is slightly negative. You know this because cos(1.4x) decreases faster than cos(0.6x), so their difference will be negative.
Of the answer choices, you can eliminate C and D because they are not zero at x=0. You can eliminate choice B, because it is positive for values of x near zero. The only viable choice is A:
-2sin(x)sin(0.4x)
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Of course, a graphing calculator can help you figure this out. See the attachment. The given expression is plotted using a solid red line; the answer choice A is plotted using blue dots.
A graph can be helpful for finding limits of integration.
The volume can be found using cylindrical shells of height (x-0.5x^2) and radius (3-x).
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The parabola whose area is shaded purple is the difference between the curves y=x and y=0.5x^2. The area under the parabola shaded purple is
(2/3)*height*width = (2/3)*(0.5)*2 = 2/3
The volume is that area multiplied by the circumference of the circle about which its centroid is revolved. That circle has radius 2, so its circumference is 4π. Then the volume is
V = (2/3)*4π = 8π/3
The BEST estimate for the capacity of a bath tub is option B)-50 gallons
50 fluid ounces is a very smaller unit so it cannot be true.
50 cups is also small as compared to a standard bath tub that can hold almost 60-80 gallons of water.
50 pints is almost 6.25 gallons which is also very less amount of water as compared to the bath tub.
Hence, option B is correct estimate.
Answer:
1/4
Step-by-step explanation:
1/3 - 1/12 = 4/12 - 1/12 (LCM)
= 3/12
=1/4 (simplified)