Answer: The height of the building = 56 feet.
Step-by-step explanation:
Let AB be the height of the building and BC be the distance of the car from the building on the ground.
Now , ∠ C = 32° [Alternate interior angles ]
According to the trigonometry,
Hence, the height of the building = 56 feet.
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The image I saw was a paper with 90° edges. the 90° was cut into 2, 75° and x.
x = 90° - 75° = 15°
Interior angles of a triangle should equal 180°. The other corner of the paper is part of the triangle. It has a measure of 90°
The two angles are 15° and 90°. To find the remaining unknown angle, we deduct the two angles from 180°
3rd angle = 180° - 15° - 90°
3rd angle = 180° - 105°
3rd angle = 75°
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.
9514 1404 393
Answer:
12 dimes
Step-by-step explanation:
Let q represent the number of quarters. Then the number of dimes is 16-q and the total value is ...
0.25q +0.10(16 -q) = 2.20
0.15q +1.60 = 2.20 . . . . . . . simplify
0.15q = 0.60 . . . . . . . . subtract 1.60
q = 4 . . . . . . . . . . . divide by 0.15
16-q = 12
There are 12 dimes in the collection.
Putting the two numbers together in fraction form of a ratio, we have 76/19. We know that something multiplied by 19 will equal to 76.
When we try to multiply 4 and 19 together, we have our nice answer 76. We then replace out values in the original ratio, in which we get the final answer of 4:1, 4/1, or 4 to 1.
