Polygon ABCD has vertices A(1,3) , B(1,6) , C(4,6) , and D(5,2) .

Mathematics

1 answer:

Bond [772]2 years ago

5 0

Answer:

check below for explanation.

explanation:

➢ Given coordinates:

A( 1, 3 )
B( 1, 6 )
C( 4, 6 )
D( 5, 2 )

➢ after a dilation with a scale factor of 1/2:

A( 1, 3 ) ÷ 2 ☛ A'(0.5,1.5)
B(1, 6 ) ÷ 2 ☛ B'(0.5, 3)
C( 4, 6) ÷ 2 ☛ C'( 2, 3 )
D( 5, 2) ÷ 2 ☛ D'( 2.5, 1)

➢ Plot the after dilation coordinates on the graph:

check the image below:

You might be interested in

What function is shown in the graph above?

Verizon [17]

By definition of <em>linear</em> functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

<h3>What kind of function represents the graph?</h3>

Graphically speaking, <em>linear</em> functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). <em>Linear</em> functions are characterized by slope and intercept:

y = m · x + b (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of <em>linear</em> functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

To learn more on linear functions: brainly.com/question/14695009

#SPJ1

8 0

2 years ago

Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t

Neporo4naja [7]

Answer:

$V=61.66$

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

$V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx$

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

$f(x)=g(x)\\ln(x)=\frac{1}{2}x-2$

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

$R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\$