Answer:
Olive
Step-by-step explanation:
Olive runs faster :).
Answer:
Step-by-step explanation:
Using the hint, write a and b in the following prime factorization:
where for i ≠ j.
Then by the formulae for gcd(a,b) and lcm(a,b) we know that:
Note that the expression for all i, since if the minimum is, <em>without loss of generality</em>, , then the maximum must be , and viceversa. Then, it is straightforward to verify that when we multiply gcd(a, b) and lcm(a, b) its prime factorization matches the prime factorization of ab, and so we can see the equaility holds:
Answer:
Step-by-step explanation:
we know that
The tangency point on the x-axis is (r,0)
The tangency point on the y-axis is (0,r)
Find the slope of the line containing the points of tangency
Remember that the equation of the line into slope intercept form is equal to
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem we have
substitute
Direct variation is y = kx
Inverse variation is y = k/y
if z varies directly with x, then the equation would be z = kx
if z varies inversely with y^2 then the equation would be z = k/y^2. Combining, these two, we have z = kx/y^2
We use the first set of values to find the constant k:
x = 2, y = 5, z = 8:
8 = 2x/25, k = 100. Now we use the second set of values to find z:
x = 4, y = 9, k = 100 and z is unknown:
z = (4X100)/9^2
z = 400/81--> this is your final final answer.
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