Line segment XY is tangent to circle Z at point U. If the measure of is 84°, what is the measure of ? 42° 84° 96° 168°
2 answers:
Answer:
The measure of angle YUV is equal to
Step-by-step explanation:
see the attached figure to better understand the problem
we have that
-----> given problem
so
------> by central angle
we know that
The triangle UZV is an isosceles triangle
because
so
-----> bases angle of the isosceles triangle
Remember that
The sum of the internal angles of a triangle is equal to
so
substitute and solve for m<ZUV
------> by complementary angles
solve for m<YUZ
You might be interested in
Answer:
- Base Length of 84cm
- Height of 42 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume,
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 84cm
- Height of 42 cm.