This is question of geometric sequence, equation of growth for this matter. The explicit formula for geometric sequence is given by:
a(n) = a(0)r^(n-1)
where;
a(n) = population after time "n"
a(0) = Initial population = 65
n = time = 5 weeks
r = common ratio = (100+30)% = 1.3
Substituting, beetles after 5 weeks will be;
a(5) = 65*1.3^(5-1) = 185.65 ≈ 186 beetles
The area of a square is the square of the length of its side. Here, we're told that the side of each square is equal to the radius (r) of the circle. Then the area of each square is
.. Asquare = r^2
There are 3 of them, so their total area is
.. Aall_squares = 3*r^2
The area of a circle is given by the formula
.. Acircle = π*r^2 . . . . . where r represents the radius of the circle
Fernie wants to compare the area of the 3 squares to that of the circle. We know that the value of π is about 3.1416, a little more than 3, so we have
.. Aall_squares = 3*r^2
.. Acircle ≈ 3.1416*r^2
We notice that 3.1416 is more than 3, so the area of the circle is greater than the area of Fernie's 3 squares.
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It is not clear to me that Fernie's drawing will explain the formula A = π*r^2, unless it can somehow be used to show that the parts of each square that are outside the circle add up to an amount that is slightly less than the uncovered part of the circle.
Answer:
The value of k is 4.
Step-by-step explanation:
To find the missing coordinate, we can use the slope equation and plug in all known values.
m(slope) = (y2 - y1)/(x2 - x1)
-1 = (k - 0)/(-2 - 2)
-1 = k/-4
Now we can solve using cross multiplication.
-1 = k/-4
k*1 = -1*-4
k = 4
Answer:
Step-by-step explanation:
To get the shortest distance from a point to a line, we need to find a perpendicular line that intersects the line and also intersects the line. We know the slope of the line will be 1/2, but to find the y-intercept, we can just plug it into the point because we already know it will be on the line.
-3 = 1/2(-2)+c
-3 = -1+c
-2 = c
Now, we know the slope and the y-intercept, and since it will intersect the other line, we can set it equal to the other lines formula:
1/2x-2 = -2x+6
5/2x=8
x=16/5
Now, plugging this value of x into any of the equations, we can find the y-coordinate:
16/5(1/2)-2 = -2/5
We have the point (16/5, -2/5)
Now, we need to find the distance between (-2, -3) and (16/5, -2/5)
Plugging into distance formula:
= 
Answer:
x = 13
Step-by-step explanation:
m∠ABC + m∠CBD = 180° {linear pair}
3x + 43 + 6x + 20 = 180
3x + 6x + 43 + 20 = 180
9x + 63 = 180
9x = 180 - 63
9x = 117
x = 117/9
x = 13
