Answers:
- Part (a) 10*sqrt(13)
- Part (b) 10*sqrt(5)
Those values are exact. They approximate to:
10*sqrt(13) = 36.0555
10*sqrt(5) = 22.3607
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Explanation:
Part (a)
If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.
Apply the pythagorean theorem
a^2 + b^2 = c^2
20^2 + 30^2 = c^2
400 + 900 = c^2
1300 = c^2
c^2 = 1300
c = sqrt(1300)
c = sqrt(100*13)
c = sqrt(100)*sqrt(13)
c = 10*sqrt(13) .... exact length
c = 36.0555 ...... approximate length
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Part (b)
If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.
Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.
a^2 + b^2 = c^2
20^2 + b^2 = 30^2
400 + b^2 = 900
b^2 = 900-400
b^2 = 500
b = sqrt(500)
b = sqrt(100*5)
b = sqrt(100)*sqrt(5)
b = 10*sqrt(5) ..... exact length
b = 22.3607 ....... approximate length
20.8478066 (or 20.85%)
you do 480.77 minus 380.54 and it comes out to 100.23 and then you do 100.23/480=x/100 (discount/original=percent/100) and you multiply 100.23 by 100 and it comes to 10023 and you do 10023 divided by 480.77 and it comes out to 20.8478066 or 20.85%
Answer:
Step-by-step explanation:
Carry out the indicated multiplication. We get:
18a^3 - 12a^2b + 8a^2b^2 - 2b
This is as far as we can go until you've explained the ' ? ' sign in your expression.
Answer:
6 seconds
Step-by-step explanation:
In second 1, the distance that separates them is 80 cm
Then, in second 2, it is an additional 76 cm which is 156
then 72, etc. etc.
From that, we can continue adding until we the total sum is 420.
80+76+72+68+64+60=420
That's 6 seconds
Not the most elegant solution but I think one of the simplest.
