Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
===============================================
Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
-------------------
For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
Answer:
Step-by-step explanation:
In order to get the answer to this question you need to turn the scientific notations into standard form then subtract the two standard forms.
Turn the notations into standard form:
Turn into notation form:
Hope this helps.
First, we are going to find the radius of the yaw mark. To do that we are going to use the formula:
where
is the length of the chord
is the middle ordinate
We know from our problem that the tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet, so
and
. Lets replace those values in our formula:
Next, to find the minimum speed, we are going to use the formula:
where
is <span>drag factor
</span>
is the radius
We know form our problem that the drag factor is 0.2, so
. We also know from our previous calculation that the radius is
, so
. Lets replace those values in our formula:
mph
We can conclude that Mrs. Beluga's minimum speed before she applied the brakes was
13.34 miles per hour.
307.85
-40
-9.50
-41.75
+23.75
-4.62
=235.73$