Answer:
79 feet per second
Step-by-step explanation:
Convention: upwards positive
s = ut + 0.5at²
94 = 2u + 0.5(-32)(2²)
2u = 158
u = 79 feet/second
Step One
======
Find the length of FO (see below)
All of the triangles are equilateral triangles. Label the center as O
FO = FE = sqrt(5) + sqrt(2)
Step Two
======
Drop a perpendicular bisector from O to the midpoint of FE. Label the midpoint as J. Find OJ
Sure the Pythagorean Theorem. Remember that OJ is a perpendicular bisector.
FO^2 = FJ^2 + OJ^2
FO = sqrt(5) + sqrt(2)
FJ = 1/2 [(sqrt(5) + sqrt(2)] \
OJ = ??
[Sqrt(5) + sqrt(2)]^2 = [1/2(sqrt(5) + sqrt(2) ] ^2 + OJ^2
5 + 2 + 2*sqrt(10) = [1/4 (5 + 2 + 2*sqrt(10) + OJ^2
7 + 2sqrt(10) = 1/4 (7 + 2sqrt(10)) + OJ^2 Multiply through by 4
28 + 8* sqrt(10) = 7 + 2sqrt(10) + 4 OJ^2 Subtract 7 + 2sqrt From both sides
21 + 6 sqrt(10) = 4OJ^2 Divide both sides by 4
21/4 + 6/4* sqrt(10) = OJ^2
21/4 + 3/2 * sqrt(10) = OJ^2 Take the square root of both sides.
sqrt OJ^2 = sqrt(21/4 + 3/2 sqrt(10) )
OJ = sqrt(21/4 + 3/2 sqrt(10) )
Step three
find h
h = 2 * OJ
h = 2* sqrt(21/4 + 3/2 sqrt(10) ) <<<<<< answer.
Because the equation does not have a y-intercept, the first plotted point is at (0,0). From there, since the slope of the line is 3/4, you would count right 3 and move up 4. Plot the point and continue with the pattern. To get the left side of the line, move left 3 and down 4.
Answer:
$158.85
Step-by-step explanation:
$325.58-$166.73=$158.85
<h3>
Answer: Rs 2500</h3>
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Explanation:
Compute the simple interest on a deposit of x
The per annum (p.a.) interest rate is r = 0.12 from the 12% value mentioned.
We do so over t = 2 years
i = p*r*t
i = x*0.12*2
i = 0.24x
Let A = 0.24x
Do the same for the compound interest. We'll have n = 1 to reflect annual compounding.
i = p*(1+r/n)^(n*t) - p
i = x*(1+0.12/1)^(1*2) - x
i = 1.2544x - x
i = 0.2544x
Let B = 0.2544x
We're told that "The simple interest on a sum of money in 2 years is Rs 36 less than the compound interest compounded annually"
This means the interest earned in the simple interest (value A) is Rs 36 less than the amount earned with quantity B
So,
A = B-36
0.24x = 0.2544x - 36
0.24x - 0.2544x = -36
-0.0144x = -36
x = -36/(-0.0144)
x = 2500
The amount invested or deposited is Rs 2500
