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Man's height / Man's shadow = Building's height / Building's shadow
Convert all to inches
69 / 168 = h / 600, where h is the height of the building.
h = (600)(69) / 168
divide h by 12 to convert to feet again
20.5 ft


Australian bedroom are 2.3 meters which is 7.5 feet
5 feet 11 inches/7 feet = 8 feet/x (mine)
71 inches/84 inches in shadow = 96 inches building height/x
cross multiply 84 inches in shadow X 96 inches building height = 8064
8064/71 = 113.57746478873239436619718309859
Divide 113.57746478873239436619718309859 by 12 = 9.4647887323943661971830985915493

Now, his:

His height/His shadow’s height = 8 feet building’s height / 9.46…………for building’s shadow

X/6.5 feet = 8 feet/9.46………..

X/78 inches = 96 inches/9.46…….

96 inches multiplied by 78 inches = 7488

7488/9.4647887323943661971830985915493 = 791.14285714285714285714285714288

791.14285714285714285714285714288 divided by 12 inches = 65.928571428571428571428571428573

65.928571428571428571428571428573 divided by 12 inches = 5.4940476190476190476190476190478

..

34) 56

Circumference of Circle O = 16p inches.
BC = 3/4 of the length of diameter AD
CE = 4 inches


r = 8 (half of diameter)
d = 16pi/pi = 16

AD = Diameter = 16
BC = 3/4 of AD so, BC is Diameter/4 = 4, since we want
3/4, then 3 X 4 = 12
so, BC is 12 inches
AD is 16 inches
CE is 4 inches
Area = 16(2) + 12(2) = 56 Square Inches.



35) $7,4699.04785 is not the correct answer.
5,583.86 is the correct answer because:



Initial Amount = $5000
Interest Rate = 3.75% = 0.0375
Interest in $s = $5000 X 0.0375 = $187.50
Total Amount after 1 year = $5000 + $187.50 = $5187.50

2nd Amount = $5187.50 X 0.0375 = $194.54125
Total Amount after 2 years = $5187.50 + $194.54125 = $5382.03125

3rd Amount = $5382.03125 X 0.0375 = $201.826171875
Total Amount after 3 years = $5382.03125 + $201.826171875 = $5583.857421875
Which really is $5583.86 if you round it up.

P1: 60/60
p2: 6/6
p3: 3/9
p4: 12/12
= 81/87

Unit Circle

What is the domain of g(x) = square root of X square + 2X - 8???

(1) {x|x greater than or equal to 4 or X is less than or equal to -}
(2) {x|x greater than or equal to 2 or X is less than or equal to -4}

g(x)
= sqrt(x^2 + 2x - 8)
= sqrt((x + 4)(x - 2))

For g(x) to be real, x^2 + 2x - 8 must be >= 0
Thus, (x + 4)(x - 2) >= 0
We have x<= -4 or x>= 2

If you want to check, you can substitute a number less than -4, a number between -4 and 2, as well as a number greater than 2 into x^2 + 2x - 8

Hence, the answer is (2).

How do i solve this trigonometry question which involves Sigma?

Barron's Regents book is not as specific in explaining how to solve several problems.

The Sigma's bottom notation is (i=1), notation above is 8. So it's Sigma E, above is 8, bottom is i = 1 and then (3i - i^2).

I know it's -96, but have no clue how it came to be -96.



ANSWER:
Here's how you do it step by step. :)

Sigma always denotes SUM. Therefore, you have to add all the values of the expression by substituting i = 1 to 8.

For,

i = 1: 3(1) - (1)^2 = 3 -1 = 2
i = 2: 3(2) - (2)^2 = 6 - 4 = 2
i = 3: 3(3) - (3)^2 = 9 - 9 = 0
i = 4: 3(4) - (4)^2 = 12 - 16 = -4
i = 5: 3(5) - (5)^2 = 15 - 25 = -10
i = 6: 3(6) - (6)^2 = 18 - 36 = -18
i = 7: 3(7) - (7)^2 = 21 - 49 = -28
i = 8: 3(8) - (8)^2 = 24 - 64 = -40

Therefore, the sum is: 2 + 2 + 0 + (-4) + (-10) + (-18) + (-28) + (-40) = -96.

Hope this helps.

The roots of the equation 3x^2 - 2x = 6 are?

(1) real, irrational, and unequal
(2) real, rational, and equal
(3) real, rational, and unequal
(4) imaginary

The answer is (3)

If logb2 = r and logb3 = s, then express logb9 square root of 2 in terms of r and s. The correct answer is 2s + 1/2 r but how is the answer that?

r
= logb (2)
= logb (sqrt(2))^2
= 2*logb (sqrt(2))

Thus, logb (sqrt(2)) = r/2

logb 9*(sqrt(2))
= logb 3*3*(sqrt(2))
= logb (3) + logb (3) + logb (sqrt(2))
= s + s + r/2
= 2s + r/2

Note that:
1) log a^b = b*log a for a > 0
2) log a*b = log a + log b for a,b > 0