Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
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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.
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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:
The year is 2020.
Step-by-step explanation:
Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.
Given:
Initial population is, 
Growth rate is, 
Final population is, 
A population growth is an exponential growth and is modeled by the following function:
Taking log on both sides, we get:
Plug in all the given values and solve for 'x'.
So, for 
, the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.
Therefore, the tenth year after 2010 is 2020.
For A. the muddy water will slowly begin to decrease because it's been left out in the sun, some of the water will begin to evaporate.
(I don't know about B, or C, but I tried my best on A.)
Make sure to put in your own words. :)
Answer:
17.5
Step-by-step explanation:
Given that the variables x and y have a proportional relationship.
i.e. y is directly proportional to x or can be written as
y = mx where m is the constant of proportionality.
When x =2, y =7
Substitute this to get the value of m.
7 =2m or m = 3.5
Thus the relationship between x and y is
y = 3.5x
So when x=5, y = 3.5(5) = 17.5
