The area of the region that is not shaded in the diagram is determined through the following solution:

A = (1 − (60°/360°)*π) * (10 ft ) ^2 A = 56*π*100 [ft2] A = 250/3 π [ft2]
A = 262 [ft2]

5 0

3 years ago

The difference of two numbers is 16 the greater number is five less than four times a small number find the two numbers

Elis [28]

Answer:

The numbers are 23 and 7

Step-by-step explanation:

1. Set up the equations

Let x = the greater number

and y = the smaller number. Then

(1) x - y = 16

4y = 4 times the smaller number and

4y - 5 = 5 less than 4 times the smaller number. Then

(2) x = 4y - 5

You have a system of two equations:

$\begin{cases}(1) & x - y = 16\\(2) & x = 4y - 5\end{cases}$

2. Solve the equations

$\begin{array}{lrcll}(3) & 4y - 5 - y & = & 16 &\text{Substituted (2) into (1)}\\& 3y - 5 & = & 16 &\text{Simplified}\\ & 3y & = & 21 &\text{Added 5 to each side}\\(4) &y & = & \mathbf{7} &\text{Divided each side by 3} \\& x - 7 & = & 16 & \text{Substituted (4) into (1)}\\& x& = & \mathbf{23} & \text{Added 7 to each side}\\\end{array}$

The larger number is 23; the smaller number is 7.

3. Check

$\begin{array}{rclcrcl}23 - 7& = & 16 & \qquad &23&=&4(7) - 5\\16 & = & 16 & \qquad &23& = &28 - 5\\&&& \qquad &23& = &23\\\end{array}$

OK.

3 0

3 years ago