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Prove that
im (x→-4) x^2=16 .using epsilon and delta property.
find the equation of the parabola whose end points of length are (-7/2,3) and (-7/2,-5) passes through (-2,-5).
Hello expert ,can you tell me any reason that empty set is the subset of every set.
Hi Expert mathematician can you tell me about the difference of constant and parameter.Best Regards
A conical tank (with its tip down and the circular base parallel to and above the ground) is filling with water in such a way that the height of the water is increasing at a rate of 0.1cm/hr at the instant that the height of the water level is 10cm. If the tank has a radius of 12cm and a height of 30cm, find how fast the area corresponding to the top of the water level is increasing at this instant.
1 A cone-shaped drinking cup is made from a circular piece of paper with radius R by cutting out a “sector” and joining the edges CA and CB. Set up a function representing the volume of the drinking cup as a function of one variable only. Then, use calculus to determine the dimensions of the drinking cup that yield the greatest volume. Be sure to verify that your answer corresponds to a maximum. Determining the an expression for the radius of the new circular cone in addition to an expression for the height of the cone will be critical in answering the question. Note, the size of the sector that can be removed is not fixed. As its size changes, so does the angle theta and so does the resulting radius and height of the cone that is formed by bringing the edges CA and CB together.
(Hint, to better see the geometry pertaining to the problem, draw a large circle on a piece of paper and cut out a sector. )
I have three known points (0,0) (5,26) (12,312) how do i find the curve from 0 to 312?
For example. If i want to plug in x-7 what is y?
1.Graph one arch of the cycloid x= t – sin t, y = 1 – cos t .
2. Find the arc length of one arch of the above cycloid.

Using Maple
4^-1/2=3/4
If the following costs are incurred on sales of £18,500:

Staff Wages - £3367

Management Salary - £2250

What are the following percentages? (To 1 decimal place)


Staff Costs
Required
17.8%
19.6%
18.2%
30.4%
12.2%


Management Costs
Required
30.4%
15.2%
21.3%
8.4%
12.2%


Total Employment Costs
Required
30.4%
27.2%
32.5%
21.9%
36.8%


Question 3.
If a pizza costs £2.85 to produce and is sold to the guest for £9.95, what percentage gross profit is made from this dish? (To 1 decimal place)
Required
64.3%
81.2%
72.8%
71.4%
69.2%


Question 4.
What is the VAT amount on an item that sells for £8.50
Required
??1.92
??1.42
??1.27
??1.17
??0.98

Question 5.
A case of 24 bottles of Lager costs £15.84 from our suppliers and we sell each individual bottle for £2.95.


What percentage profit do we make on each bottle?
Required
63.2%
77.6%
76.7%
22.4%
36.8%


How much cash profit is made on the whole case?
Required
£54.96
£70.80
£62.10
£48.34
£69.21

Question 6.
The Belvedere Arms takes £11,800 in drink sales and £5,600 in food sales in a week. In the same week the pub delivers £8,496 profit on drink and £3,640 profit on food. The week's sales budget is £16,200.

What are: (To the nearest whole number)


Total Sales
Required
£17,400
£12,136
£21,300
£29,536
£18,500


Performance Against Sales Budget
Required
Up by 6.9%
Down by 7.4%
Flat
Up by 7.4%
Down by 6.9%


Food GP%
Required
56%
153%
65%
178%
Impossible to say


Drink GP%
Required
72%
49%
151%
138%
Impossible to say


Total GP%
Required
143%
127%
62%
70%
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