For whatever reason, Brainly questions are often missing the first character. Here, we assume it is A, so that the intended statement is ABCD~EFGH.
FG = BC*(EH)/AD = 15*60/45 = 20 . . . . inches
A growth rate equation has a general form of:
f(x) = P (1 + r)^x
Where,
P = present value
r = rate of growth
x = number of years
If we write the given equation on that form, it would be:
f(x) = 4 (1 + 3)^x
Therefore we can see that the population’s growth rate is
300% per year. To make this formula to an equivalent of three times a year (3x),
we have to find the new r.
f(x)_3 = 4 (1 + r)^3x
To calculate this, we must take note that the expression or
value of (1 + r)^x must be constant. Therefore equate this with 4^x.
(1 + r)^3x = (4)^x
Taking the logs of both sides:
3x log (1 + r) = x log 4
Cancelling x:
3 log (1 + r) = log 4
3 (1 + r) = 4
1 + r = 4/3
r = 0.33
Therefore the new growth rate is 0.33 or 33%. (ANSWER)
And, the new correct function is:
f(x)_3 = 4 (1 + 0.33)^3x
or
f(x)_3 = 4 (1.33)^3x (ANSWER)
Answer:
Parallel: 
Perpendicular: 
Step-by-step explanation:
Parallel lines have the same slope.
Perpendicular lines have opposite reciprocal slopes.
The point slope form of a line is:
where 
is a point on the line and 
is the slope.
To find the slope we will first have to find the slope of the given line.
We are going to put it into slope-intercept form 
because it tells us the slope,m, which is what we need.
Parallel lines will have the same slope, .
Perpendicular lines will have the opposite reciprocal slope: 
.
So let's put 
into form by solving for 
.
Subtract 
on both sides:
Divide both sides by -2:
Simplify:
or
.
So the slope is 1/2 for the given equation.
Our parallel line will also have slope 1/2.
Our perpendicular line will have slope -2.
Let's move onto finding these equations starting with the parallel one.
Plug in 
and 
:
Now the perpendicular one:
Plug in 
and :
<h3>
Answer: 1589.65 miles</h3>
==============================================
Explanation:
The degree of separation from the two cities is 30-7 = 23 degrees.
Let's say the point C is at the center of the earth. This would mean angle BCA is 23 degrees.
Any longitude line helps form what is known as a great circle or orthodrome. This is a math term that describes a circle that is centered at the same location as the sphere's center. Imagine that you can wrap a string around the earth and this string only follows this particular longitude line. This string is effectively a vertical equator in a way. The question is: what is the length of this string?
Well that would be the circumference of the circle with radius 3960 miles because the longitudinal circle has the same radius as the sphere.
That approximates to...
C = 2*pi*r
C = 2*pi*3960
C = 24,881.4138164311
C = 24,881.41
So a bit less than 25 thousand miles. I used the calculator's stored version of pi rather than something like 3.14 to get the best accuracy possible. This is the full string's length if we want to travel the entire distance around the globe but stay entirely on this particular longitude line
We don't want the full string's length. Instead, we want just a fractional portion of it. Specifically, we want 23/360 of it because of the central angle of 23 degrees. This will give us the distance between the two cities.
So (23/360)*24,881.4138164311 = 1,589.64588271642
This then rounds to 1589.65 when rounding to the nearest hundredth.
The distance between the two cities is approximately 1589.65 miles
This is comparable to the driving distance from Los Angeles, CA to Houston, TX (approximately 1547 miles).
