Answer:
I18 - xI such that x < 18.
ok, first let's what happens if x = 18:
I18 - xI = I18 - 18I = 0
So, at the moment we have the condition:
I18 - xI > 0.
now, if x is a really large negative number, suppose, x = -100
I18 + 100I = I118I = 118
So, as x can freely move in the negative range, we can see that I18 - xI can be any positive number, so the only restriction that we have is:
I18 - xI > 0.
This means that the domain is:
D = (-∞, 18)
and the range is:
R = (0, ∞)
Answer:
Correct answer: V₁ boat = 16 km/h and V₂ current = 4 km/h
Step-by-step explanation:
If we take speed (velocity) of the boat as V₁ and speed of the current V₂
Let us form equations:
Traveling down the current V₁ + V₂ = 60/3 = 20 km/h
Traveling against the current V₁ - V₂ = 60/5 = 12 km/h
V₁ - V₂ = 12
V₁ + V₂ = 20
If we add up the left and right sides of the equations we get:
2 V₁ = 32 => V₁ = 32/2 = 16 km/h
from the second equation we get:
V₂ = 20 - V₁ = 20 - 16 = 4 km/h
V₂ = 4 km/h
God is with you!!!
Answer:
1287
Step-by-step explanation:
The number of combinations of 13 diamonds taken 5 at a time is ...
13C5 = 13·12·11·10·9/(5·4·3·2·1) = 13·11·9 = 1287
Start with 180.
<span>Is 180 divisible by 2? Yes, so write "2" as one of the prime factors, and then work with the quotient, 90. </span>
<span>Is 90 divisible by 2? Yes, so write "2" (again) as another prime factor, then work with the quotient, 45. </span>
<span>Is 45 divisible by 2? No, so try a bigger divisor. </span>
<span>Is 45 divisible by 3? Yes, so write "3" as a prime factor, then work with the quotient, 15 </span>
<span>Is 15 divisible by 3? [Note: no need to revert to "2", because we've already divided out all the 2's] Yes, so write "3" (again) as a prime factor, then work with the quotient, 5. </span>
<span>Is 5 divisible by 3? No, so try a bigger divisor. </span>
Is 5 divisible by 4? No, so try a bigger divisor (actually, we know it can't be divisible by 4 becase it's not divisible by 2)
<span>Is 5 divisible by 5? Yes, so write "5" as a prime factor, then work with the quotient, 1 </span>
<span>Once you end up with a quotient of "1" you're done. </span>
<span>In this case, you should have written down, "2 * 2 * 3 * 3 * 5"</span>
