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An object starts from rest with a constant acceleration of 10 ft/s² along a straight road. Determine the velocity after 3.5 sec, b) the average velocity for the 3.5 seconds interval, and c) the distance travelled in this given time.
A. Tell whether each given function has a solution on the indicated closed interval. Prove using the Intermediate value theorem.
1. f(x)=3x²+2x²;[-1,1]
2. f(x)= 2-x²/x²;[-3,-1]
B. Sketch the graph of the following functions and then find the absolute extreme values of each of the given interval.
1.f(x)=√x²-25;[5,10]
2. f(x)=-1/x²;[0.5,2]
C. A restaurant's profit function (in hundreds) for hamburgers is given by the function P such that P(x)=1.22x-x²/30,000-4,000,where 0≤x≤20,000.
1. How many hamburgers does the restaurant need to sell to yield the maximum profit?
2. What is the maximum profit from the sale of hamburger ?
An automobile and a truck start from rest at the same instant, with the automobile
initially at some distance behind the truck. The truck has a constant acceleration of 2
m/s2 and the automobile at an acceleration of 3 m/s2
. The automobile overtakes the
truck after the truck has moved 75 m. Try to draw the figure.
a) How long does it take the auto to overtake the truck?
b) How far was the auto behind the truck initially?
c) What is the velocity of each when they are abreast?
What is grapichal method of 2x-3y=7; 3x+y=5
B. Sketch the graph of the following functions and then find the absolute extreme values of each of the given interval.
1.f(x)=3-2/5x;[-4,0]
2.f(x)=x-3/4+x;[-3,1]
C. Let f(x)=2x+1. Determine if the Intermediate value theorem applies to f on the closed interval [-3,4]for k=1.
1. Given: List1[‘Bob’, ‘Andy’, ‘Roy’, ‘Mike’, ‘Kim’]
print the first element
The height of SHS is normally distributed with a mean of = 150 cm and a standard deviation of = 10 cm.
a) Sketch a normal curve that describes this distribution.
b) Approximately what percent of these students have a height greater than 170 cm?
Samples of 3 cards are drawn from a population of five cards numbered from 1-5.
1. How many are the possible outcomes?
2. What are the possible means?
3. What is the probability of getting 4 as a mean?
4. What is the probability of getting 2 as a mean?
5. What is the probability of getting 3.33 as a mean?
A 1205 kg car is running a speed of 35 m/s along a level road. How large a constant retarding force is required to stop it in 15 s?
Given a population mean weight for baggage of 62 kg and a standard deviation of 8 kg. A sample of 50 baggage is taken. What is the probability that the sample mean differs from the population mean by at most 1kg?
#340153 on Dec 2023