Answer:
(x - 6)² + (y - 7)² = 4
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r²
Given center(h,k) = (6,7)
h = 6
k = 7
Dimeter = 4 --
radius, r =
= 2
(x - h)² + (y - k)² = r²
(x - 6)² + (y - 7)² = 2²
(x - 6)² + (y - 7)² = 4
Answer:
We have 40% antifreeze and 70% antifreeze and we need to make 240 liters of 64% antifreeze.
We set up 2 equations where "f" is the 40 % and "s" is the 70%
A) f + s = 240
B) .40f + .70s = (.64 * 240) (or 153.6)
To solve both equations we multiply A) by -.40
A) -.40 f - .40 s = -96.00 then we add this to B)
B) .40f + .70s = 153.60
.30s = 57.6
s = 192
f = 48
48 liters of 40% = 19.20 liters of antifreeze
192 liters of 70% = 134.40 liters of antifreeze
That equals 153.60 liters of antifreeze in a TOTAL liquid amount of 240 liters.
Double Check
153.60 / 240 = 64% antifreeze.
Step-by-step explanation:
Answer:
5√2
Step-by-step explanation:
√8 + √18
We first have to find what is the largest perfect square that goes into √8:
4 is the largest, so therefore → √8 gives you 2√2:
Work: √4 * √2 → 2 * √2 → 2√2
Now we have to find what is the largest perfect square that goes into √18:
9 is the largest, so therefore → √18 gives you 3√2:
Work: √9 * √2 → 3 * √2 → 3√2
Because 2√2 and 3√2 have the same "base" of √2, they can be added together:
2√2 + 3√2 = 5√2 (The "bases" are to be left alone!)
Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.
Answer:
Step-by-step explanation:
if a person is not a hockey player, they are not a prof athlete
if a person is a hockey player, they are a prof athlete
if a person is not a prof athlete, then they r not a hockey player