Answer:
6194.84
Step-by-step explanation:
Using the formula for calculating accumulated annuity amount
F = P × ([1 + I]^N - 1 )/I
Where P is the payment amount. I is equal to the interest (discount) rate and N number of duration
For 40 years,
X = 100[(1 + i)^40 + (1 + i)^36 + · · ·+ (1 + i)^4]
=[100 × (1+i)^4 × (1 - (1 + i)^40]/1 − (1 + i)^4
For 20 years,
Y = A(20) = 100[(1+i)^20+(1+i)^16+· · ·+(1+i)^4]
Using X = 5Y (5 times the accumulated amount in the account at the ned of 20 years) and using a difference of squares on the left side gives
1 + (1 + i)^20 = 5
so (1 + i)^20 = 4
so (1 + i)^4 = 4^0.2 = 1.319508
Hence X = [100 × (1 + i)^4 × (1 − (1 + i)^40)] / 1 − (1 + i)^4
= [100×1.3195×(1−4^2)] / 1−1.3195
X = 6194.84
If it is a rhombus then you know each side is the same length, so only have to work out one side. To do this you have to use Pythagoras' theorem (a^2 + b^2 = c^2)
So take two sets of coordinates, for example, (0,3) and (5,3), a and b represent the height difference and the length difference. Therefore (5-0)^2 + (3-3)^2 = c^2
c^2 = 25
c = 5 , which would be the side of the rhombus
Answer:
m<2 = 65
Step-by-step explanation:
The measures of angles 1 and 3 should be added together resulting in 115 degrees, and all triangles equal 180 degrees. Therefore, to find m<2, you have to subtract 115 from 180 resulting in a measure of 65 degrees.
Step-by-step explanation:
The value of all the angles in a triangle add up to 180.
So to find x do 180-(66+52)
The angle opposite of x is the same value as x
X+E or X+Z are both equal to 180.
Answer:
Ancient Greeks
Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.
Step-by-step explanation:
