Answer: 
Step-by-step explanation:
In the geometric sequence we can see each time we are dividing by 5. That is the same as multiplying by so that is the common ratio.
using pythagorean theorem
a^2 + b^2 = c^2
(12x)^2 + (16x)^2 = 10^2
square each term
144x^2 + 256x^2 = 100
combine like terms
400 x^2 = 100
divide by 400 on each side
x^2 = 1/4
take the square root on each side
x = 1/2
Answer: x=1/2
Answer:
Naomi had the correct measurement the ring weighed 0.625 carats
Step-by-step explanation:
* The diamond ring weighed 5/8 carats
- To know who is right lets change the fraction 5/8 to a decimal number
∵ 5/8 means 5 ÷ 8
- 5 is smaller than 8 so we will multiply it by 10 and
insert decimal point in the quotient (answer of division)
∴ It will be 50 ÷ 8 = 6 and remainder 2/8 ⇒ 1/4
∴ The quotient = 0.6 and remainder 1/4
- 1 is smaller than 4 so we will multiply it by 10
∴ It will be 10 ÷ 4 = 2 and remainder 2/4 ⇒ 1/2
∴ The quotient = 0.62 and remainder 1/2
- 1 is smaller than 2 so we will multiply it by 10
∴ It will be 10 ÷ 2 = 5 without remainder
∴ The quotient = 0.625
* Naomi had the correct measurement the ring weighed 0.625 carats
Answer:
Step-by-step explanation:
We have that:
When we substitute n=1, we get:
When we substitute n=2 we get:
When we substitute n=3, we get:
When we substitute n=n+1, we get:
Now
We expand and simplify to obtain:
Answer:
we have:
=> r²h = 10.18 = 9.20 = 5.36 = 6.30 = 4.45 = 12.15
=> only r²h = 5.36 satisfy the problem
=> h = 5
h = 5 r = 6
h = 5 r = 6=> d = 12
