Answer:
b = 55
d = 55
Step-by-step explanation:
Part B:
1. We can see that m∠C (25 degrees), the angle with 100 degrees, and ∠B are adjacent angles that add up to 180 degrees.
- This means that b + 25 + 100 = 180
2. (Solving equation above)
Step 1: Simplify both sides of the equation.
Step 2: Subtract 125 from both sides.
Therefore, b = 55.
Part D:
1. The exterior angle theorem states that the exterior angle of a triangle is congruent to the sum of the two opposing interior angles.
- This means that 110 = d + 55
2. (Solving)
Step 1: Subtract 55 from both sides.
Therefore, d = 55.
Answer:
70 degrees
Step-by-step explanation:
Since the angles of a triangle have to add up to 180 degrees, you know that the third angle of the triangle on the left would be 180 - 60 - 65 = 55 degrees. Then, since the angles on a straight line have to add up to 180 degrees you could find one of the two missing angles of the second triangle by doing
180 - 55 - 50 = 75.
Then, you have 2 out of the 3 angles of the triangle on the right and you can find the third, the ?, by doing 180 - 75 - 35 = 70 degrees
Answer:
C. 391
Step-by-step explanation:
At
, you have
The trick to finding out the sign of this is to figure out between which multiples of
the value of
lies.
We know that
whenever
, and that
whenever
, where
.
We have
which is to say that
, an interval that is equivalent modulo
to the interval
.
So what we know is that
corresponds to the measure of an angle that lies in the third quadrant, where both cosine and sine are negative.
This means
, so
is decreasing when
.
Now, the second derivative has the value
Both
and
are negative, so we're essentially computing the sum of a negative number and a positive number. Given that
for
, and
for
, we can use a similar argument to establish in which half of the third quadrant the angle
lies. You'll find that the sine term is much larger, so that the second derivative is positive, which means
is concave up when
.
