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:
762,508 in expanded form using exponents is given as:
Given that we have to write 762, 508 in expanded form using exponents
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits
<h3><u>Write 762508 in Expanded form</u></h3>Let us first find the place value of digits
Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Place value of 7 = 700000
In 762508, 7 is in hundred-thousands place
Place value of 6 = 60000
In 762508, 6 is in ten-thousands place.
Place value of 2 = 2000
In 762508, 2 is in thousands place
Place value of 5 = 500
In 762508, 5 is in hundreds place
Place value of 0 = 0 x 10 = 0
In 762508, 0 is in tens place
Place value of 8 = 8
In 762508, 8 is in ones place
Therefore, the expanded form is given as:
700,000 + 60,000 + 2,000 + 500 + 0 + 8
<u><em>Using exponents we can write as,</em></u>
Answer:
The side length of the original square was 6 inches
Step-by-step explanation:
we know that
The area of a square is
where
b is the length side of the square
Let
x ---> the length of the original square
The area of the original square is
The length of the smaller square is
The area of the smaller square is
The area of the smaller square is 1/4 the area of the original square
so
solve for x
Multiply by 4 both sides
Solve the quadratic equation by graphing
using a graphing tool
x=2, x=6
see the attached figure
The solution is x=6 in
Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)
therefore
The side length of the original square was 6 inches
