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Algebra. Upward Bound Math and Science Rahul Raghunathan. Problem 1. You are walking up a 500. meter high hill. The trail has an incline of 12 degrees. How far will you walk to get to the top?. Solution 1.

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algebra

Algebra

Upward Bound Math and Science

RahulRaghunathan

problem 1
Problem 1

You are walking up a 500. meter high hill. The trail has an incline of 12 degrees. How far will you walk to get to the top?

solution 1
Solution 1
  • We know angle A (12 degrees) and the length of the opposite side (500. m). We want to know the length of the hypotenuse (H), so we will use the formula
  • Sine =
  • Substituting in the appropriate values,
solution 11
Solution 1

Sine 12 = 0.21

problem 3
Problem 3
  • A member on speak series allows people to join for 11$ then pay 1$ for every event attended. What is the maximum events one can attend for a total of 46$?
solution 3
Solution 3
  • We write the equation that shows the cost of speaker series related to number of events attended ( a)

46 = 1. a + 11

46 = a + 11

35 = a

problem 4
Problem 4
  • Find the Discriminant of

V + 4V + 9 = 0

solution 4
Solution 4
  • Discriminant formula is b2 – 4 (a)(c)

Where a = 1, b = 4 and C = 9

Substituting we get

= 42-4(1)(9)

= 16-36

= -20

problem 5
Problem 5
  • Add (4j+8) and (8j+3)
solution 5
Solution 5
  • Add the like terms from the quantities above
  • (4j+8) + (8j+3)

= ( 4j+8j) + ( 8+3)

= 12j+ 11

problem 6
Problem 6
  • The population of an industrial town is increasing by 5% every year. If the present population is 1 million, estimate the population five years hence.
solution 6
Solution 6
  • C. I = A-P

=

solution 61
Solution 6
  • Present population, P = 1 million, rate of increase = 5% per annumHence population after 5 years = = 1000000 (1·05)5                   = 1276280
problem 7
Problem 7
  • What is the center of the circle

x2 + y2 -144 = 0 ?

solution 7
Solution 7
  • The standard equation of a circle is

( x-h)2 + (y-k)2 = r2

Now comparing with given equation we get

( x-0)2 + (y-0)2 = (12)2

The Center of the circle is (0,0)

problem 8
Problem 8
  • A wedding planner placed orders with a florist five times in the last year . What is the standard deviaton of the number of flowers needed
  • 70 Flowers , 90 Flowers , 21 Flowers , 63 Flowers , 91 Flowers
solution 8
Solution 8
  • Mean =

= 67.12

Variance = (70-67.12)2 + (91-67.12)2+ (21-67.12)2+ (63-67.12)2+ (91-67.12)2

=3292.8

Varience =

solution 81
Solution 8
  • Variance = 658.56
  • Standard Deviation =
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