Answer:
2 sqrt(19)
Step-by-step explanation:
We know that the angle between the two hands
360 /12 *2 = 60 degrees
We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12
This is a triangle where we know 2 sides and the angle between them.
We can use the law of cosines to determine the third side
c^2 = a^2 + b^2 -2abcosC
Where C is the angle between sides a and b
a =4 and b = 10 C = 60 and we are looking for side c
c^2 = 4^2 + 10^2 -2*4*10 cos60
c^2 =16+100 - 80cos 60
c^2 = 76
Take the square root of each side
sqrt(c^2) = sqrt(76)
c = sqrt(76)
c =sqrt(4) sqrt(19)
c =2 sqrt(19)
Answer:
See attachment for rectangle
Step-by-step explanation:
Given



Required
Draw the rectangle
First, we calculate the distance between A and B using distance formula;

So, we have:





The above represents the length of the triangle.
Next, calculate the width using:


Divide both sides by 2

This implies that, the width of the rectangle is 6 units.
We have:


Since A and B are at the upper left and right, then the ther two points are below.
6 units below each of the above point are:
=> 
=> 
Hence, the points of the rectangle are:




<em>See attachment for rectangle</em>
Given functions are


The total number of ducks and swans in the lake after n months can be determined by adding the functions s(n) and d(n).





Taking 2 as common, we get

Hence The total number of ducks and swans in the lake after n months is
<h2>
Answer: x = -6</h2>
<h3>
Step-by-step explanation:</h3>
To solve for x, we have to find a way to make x the subject of the equation (get x on one side and everything else on the other side)
<h3>
</h3>
since -4 = (2/3)x [mutiply both sides by 3]
⇒ -4 × 3 = 2x [divide both sides by 2]
⇒ (-12/2) = x [simplify by dividing -12 by 2]
∴ x = -6
Answer:
(2,√21)
Step-by-step explanation:
The circle centered at the origin has equation:

Any point that satisfies this equation lie on this circle.
When x=2, we substitute and solve for y.

Take square root to get:

Therefore (2,-√21) and (2,√21) are on this circle.
From the options, (2,√21) is the correct answer