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Write a rational function whose vertical asymptotes are at x = 1, x = 3, x = -5 and whose horizontal
asymptote is at y = -4. Sketch the function on the coordinate plane and show its table of values.
Alex has a weekly budget of PhP 6, 000, which she likes to spend on foods and clothes. (1) If the price of food is PhP 150 each meal, what is the maximum meals she could buy in a week? (2) If the average price of a clothe is PhP 300, what is the maximum number of clothes she could buy in a week? (3) Draw Alex’s budget constraint with food on the horizontal axis and clothing on the vertical axis. What is the slope of the budget constraint? (4) What is Alex’s opportunity cost of purchasing a 1 meal food
Find the integral of
(y2-1) dx-2dy = 0
In class of 35 student, each student studies history and geography.twice as many study history are studying geography 1/2 as many study both subject are studying only history.illustrate the information on Venn diagram.both subject.geography.only history only one subject
Differentiate with respect to the variable
y= sin3t, find dy/dt
v= 11sin4t - 5cos5t, find dv/dt
If s = 2t3 − 21t2 +60t describes the displacement of a body at time t from a fixed point O on a straight line, find:
(A). s when t = 3 seconds
b) the values of t when the body is at rest
c) the initial velocity of the body
d) an expression for the acceleration of the body at time t
e) the initial acceleration of the body.
Differentiate y with respect to x and hence find the gradient of the tangent to the curve
y=4x2+ 3x+2 when x =2.
1. Find the area in each of the following.
a. 𝑧 = −1.47 and 𝑧 = 1.64
b. 𝑧 = −0.44 and 𝑧 = 1.82
c. The region where 𝑧 > 1.92
d. The region where 𝑧 < 2.22
2. A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 52.2 mm and a standard deviation of 2.3 mm. What percent of the butterflies had a wingspan
a. less than 48.5 mm?
b. between 50 and 55 mm?
3. A highway study of 8000 vehicles that passed by a checkpoint found that their speeds were normally distributed, with a mean of 61 mph and a standard deviation of 7 mph.
a. How many of the vehicles had a speed of more than 68 mph?
b. How many of the vehicles had a speed of less than 40 mph?
(12) Solve the pair of simultaneous equations below:-
4a − 3b = 18
a + 2b = -1
(13) The molar heat capacity of a solid compound is given by c = a + bt
Given that when and that when c = 10 when t = 50 and that c = 13 when t = 80 Find the values of a and b.
(ALL WORKING OUTS TO BE SHOWN)
Find the area in each of the following.
a. 𝑧 = −1.47 and 𝑧 = 1.64
b. 𝑧 = −0.44 and 𝑧 = 1.82
c. The region where 𝑧 > 1.92
d. The region where 𝑧 < 2.22
2. A biologist found the wingspans of a group of monary butterflies to be normally
distributed with a mean of 52.2 mm and a standard deviation of 2.3 mm. What percent of
the butterflies had a wingspan
a. less than 48.5 mm?
b. between 50 and 55 mm?
3. A highway study of 8000 vehicles that passed by a checkpoint found that their speeds
were normally distributed, with a mean of 61 mph and a standard deviation of 7 mph.
a. How many of the vehicles had a speed of more than 68 mph?
b. How many of the vehicles had a speed of less than 40 mph?
