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3. Mrs. Mariann Alvarez is approaching a stoplight moving with a
velocity of +25.0 m/s. The light turns yellow, and Ima applies the
brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then
determine the displacement of the car during the skidding process.
(Note that the direction of the velocity and the acceleration vectors
are denoted by a + and a - sign.) (3 points)
4. Riza is waiting at a stoplight. When it finally turns green, Riza
accelerated from rest at a rate of a 4.75.00 m/s2 for a time of 4.30
seconds. Determine the displacement of Riza's car during this time
period. (3 points)
1. Jo Ann and her lab partner are completing a free fall lab in physics.
Her partner drops the ball in front of the motion sensor to measure
its speed. Assuming acceleration is constant and air resistance is
negligible, how far does the object fall if it reaches a speed of 9.8
m/s? (3 points)
2. Anneth and her partner disagree about whether or not she can make
a picket fence drop to the ground in exactly 3.0 s. Her partner thinks
the fence is too light to drop that quickly, but she’s convinced it’s possible. Assuming acceleration is constant and air resistance is
negligible, from how high does she have to drop the picket fence for
the smart gate to measure its ground impact at exactly 1.0 s?
A person walks 750m due north, then 250m due east. If the entire walk
takes 13 minutes, find the person's average velocity?
An object moves along a straight line. First it travels at a velocity of
12m/s for 6s and then continues at the same direction with 20m/s for 3s.
What is its average speed?
For 10s, the velocity of a car which travels with a constant acceleration,
changes from 10m/s to 20m/s. How far does the car travel?
A cyclist covers a distance of 15 miles in 2 hours. Calculate his speed.
A boy walks at a speed of 4 kmph. How much time does he take to walk a
distance of 20 km?
A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?
If a person drives his car in the speed 50 miles per hour, how far can he
cover in 90 minutes?
In a dental surgery conducted by a country dental health team, 500 adults were asked to give the reason for their last visit to a dentist. Of the 220 who had less than a high-school education or better, 150 stated that they went for preventative reasons. Construct a 95 percent confidence interval.
- Find the eigenvalues and eigenvectors of the 3×3 matrix
A = "\\begin{bmatrix}\n 2& -1&0 \\\\\n -1& 2&-1\\\\\n 0&-1&2\n\\end{bmatrix}"
compare the series
(1+x)-3=1-3x+6x2-10x3........
with
ex= 1+x +x2/2 +x3/6............
Are they both convergent? How can you prove this?
Recall that ℤ = Integers {…,‒2, ‒1, 0, 1, 2,…}, ℝ = Real numbers and ℕ = Natural numbers {0,1,2,…}. Determine whether sets T and S are equal. Let x = 3.
Albert is a part-time real estate agent in Camilla Homes-Pagadian. For the month of April, he made a sale of P4,850,000 for two units of residential house and lot. He was given a fixed commission rate of 5% based on sale. He was employed at the same time as a Sales Operation Manager at Best Reach Sales Inc., where he is earning a monthly salary of P24,000 and given a 10% bonus if he exceeds his sales quota of P60,000 monthly. For this month, with maximum effort he sold P150,000 worth of their companies' merchandise. He is also given a certain percentage for every sale made by his subordinates which is 1% per excess of their sales quota of P50,000. His subordinates made the following sales for the period:
John
-P86,000
Mosh
Kyla
-P54,000
-P98,000
Francis
- P48,000
Requirements: Compute for the following.
1. Monthly salary
2. Straight Commission
3. Bonus Commission
4. Override Commission
5. Earnings for April
Compare the answer of the expansion of the binomial expression (1 + x)-3 = 1-3x + 6x2 -10x3 with the first four terms of a Maclaurin series for f(x) = ex ( i.e. 1+ x + x2/2 + x3/6 ).
A 5m³ tank contains helium at 380k and is evacuated from atmospheric pressure to a pressure to a pressure of 700mmHg vacuum.
Determine:
a. Mass of helium remaining in the tank
b. Mass of the helium pumped out
c. The temperature of the remaining helium falls to 8³, what is the pressure in kPa?
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