The area of the top surface of the washer is: 160.14 square mm.
<h2>Step-by-step explanation:</h2>The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)
Now, we know that the area of the annulus region is given by:
where R is the outer radius and r is the inner radius.
Here we have:
Hence, we have:
=============================================
Explanation:
Refer to the diagram below. I'm adding in points A and B, which are marked in blue. I'm also adding in variables x, y, and z.
The goal is to find HF, so let's make that equal to x. This is also equal to HB because they are radii of the same circle.
Let y be the length of segments JA and JB.
Let z be the length of segments CF and CA.
So in short we have
We know that
This must mean
Or in short,
Let's solve the first equation for z to get z = -x+13. I subtracted x from both sides.
Now plug this into the third equation to get
z+y = 22
(z) + y = 22
(-x+13) + y = 22 ... replace z with -x+13
-x+13+y = 22
-x+y+13 = 22
-x+y = 22-13 .... subtract 13 from both sides
-x+y = 9
------------------------------------
So we have this reduced system of equations of two variables and two equations
Add the equations straight down. This is the elimination property.
Doing so leads to the x terms canceling out since x + (-x) = 0x = 0
The y terms add to y+y = 2y
The terms on the right hand side add to 19+9 = 28
We are left with 2y = 28 which solves to y = 28/2 = 14.
If y = 14, then,
x+y = 19
x+14 = 19
x = 19-14
x = 5
In which we can then say
z = -x+13
z = -5+13
z = 8
Though we don't need to find z (unless you're curious about it).
Since x = 5, and we set HF equal to x, this means that HF = 5.
Given:
The quadratic equation is:
To find:
The value of k and .
Solution:
We have,
...(i)
Putting , we get
Putting in (i), we get
Splitting the middle term, we get
Here, and
.
Therefore, the required values are and
.