Sun estimated the quotient of –23.514 and –3.98 by rounding each to the nearest integer. Which equation shows the correct estima
2 answers:
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Answer:
(a) 0.107 million per year
(b) 0.114 million per year
Step-by-step explanation:
(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, and in 2014,
. Mathematically,
(b) The instantaneous rate of change is determined by finding the differential derivative at that year.
The result of differentiating functions of the firm (where
is a constant) is
. Let's use in this in finding the derivative of
.
In the year 2014, .
Answer:
m=
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is , and the leg opposite from the 60 degree angle is
In this case, a=14, n=, and m=
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=, which is equal to 7
And m=, which simplified, is equal to
Hope this helps!