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1. water flows into a conical vessel 18cm deep and 10cm in a diameter. if the rate at which the water surface is rising is 27.52mm/s, how fast is the water flowing into the conical vesel in m^3/s when the initial depth of water is 12cm?
1. the sum of two numbers is 12. find the minimum value of the sum of their cubes.
2. a triangular corner lot has perpendicular sides of lengths 120m and 160m, resectively.
a. find the area of the longest rectangular building that can be constructed on the lot with sides parallel to the street.
b. find the perimeter that closes the building.
c. if it costs P6,000.00 per square meter of floor area of the building. how much would be the approximate cost if a three-storey building is to be constructes.
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1. if y= ax^3 + bx^2 and its point of inflection is at (2,8), what are the values of a and b?
2. graph the curve and find the point of inflection: y= (9x^2 - x^3 + 6)/ (6).
3. graph the curve and find the point of inflection: y= x^3 - 3x^2 + 6.
differentiate implicity the following equations. show complete solutions
1. e^(2x+3y) =x^2 - In(xy^3)
2. x^2 y^3 = xy+x^3 + y^2 + 5
determine the critical points of f(x)=8x3+81x2-42x-8
1. Determine the critical points of each of
2. A study was conducted to determine the level of awareness of the residents of a certain municipality on the causes of hypertension. The accompanying table shows the results with respect to the gender of the respondents. Female Weight (n=48) Male Indicator (N3D32) Mean X1 X2 W 2.8 2.8 1. Intake of food high in salt 2. Intake of food high in saturated fats. 2.4 3.0 3. Caffeine consumed in more than 4 2.5 2.4 cups of coffee a day 4. Drinking too much alcohol 5. Smoking 2.9 3.0 3.2 3.2 2.8 2.8 6. Intake of drugs or medications that may increase blood presssure. 7. Lack of physical exercise 3.0 3.1 8. Stress 2.8 3.0 9. Family history of hypertension 10 Present medical conditions like kidney 2.6 2.7 2.5 2.5 disorder, diabetes mellitus and others Average a) Find the average for the male and for the female. b) Find the weighted mean, xw, for each indicator letting the n as the weight.
Determine wheather the following sets are subspaces of R
3
{(a,b,c) : a
2+ b
2+ c
2 ≤1, a,b,c ∈R}
Find the area bounded by the ff. curves and lines:
1. the loop of y2 = x 4 (3 - x)
2. 4y = x 2 – 2lnx, y = 0, x = 1, x = 4.
3. y 2 + 4x – 8 = 0, Y = 2x
4. an arch of y =1/3sin(x/3)
Find the volume generated by revolving the area bounded by the lines x + y = 5, x = 0
and y = 0, about x-axis.
