All categories

2 years ago

A function, f, is defined by the set {(2,3), (4,7),(-1,5)}.

Mathematics

1 answer:

Kitty [74]2 years ago

3 0

Answer:

{(3,2), (7,4),(5,-1)}.

Step-by-step explanation:

To find the points reflected through y=x, you are really being asked to find the inverse relation. That means we are just swapping x and y per point; like (a,b) to (b,a).

So (2,3) when reflected through y=x becomes (3,2).

(4,7) when reflected through y=x becomes (7,4).

(-1,5) when reflected through y=x becomes (5,-1).

So the inverse relation is:

{(3,2), (7,4),(5,-1)}.

You might be interested in

Please look at the picture, I need help ASAP.

forsale [732]

See below for the proof that the areas of the lune and the isosceles triangle are equal

<h3>How to prove the areas?</h3>

The area of the isosceles triangle is:

$A_1 = \frac 12r^2\sin(\theta)$

Where r represents the radius.

From the figure, we have:

$\theta = 90$

So, the equation becomes

$A_1 = \frac 12r^2\sin(90)$

Evaluate

$A_1 = \frac 12r^2$

Next, we calculate the length (L) of the chord as follows:

$\sin(45) = \frac{\frac 12L}{r}$

Multiply both sides by r

$r\sin(45) = \frac 12L$

Multiply by 2

$L = 2r\sin(45)$

This gives

$L = 2r\times \frac{\sqrt 2}{2}$

$L = r\sqrt 2$

The area of the semicircle is then calculated as:

$A_2 = \frac 12 \pi (\frac{L}{2})^2$

This gives

$A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2$

Evaluate the square

$A_2 = \frac 12 \pi (\frac{2r^2}{4})$

Divide

$A_2 = \frac{\pi r^2}{4}$

Next, calculate the area of the chord using

$A_3 = \frac 12r^2(\theta - \sin(\theta))$

Recall that:

$\theta = 90$

Convert to radians

$\theta = \frac{\pi}{2}$

So, we have:

$A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))$

This gives

$A_3 = \frac 12r^2(\frac{\pi}{2} - 1)$

The area of the lune is then calculated as:

$A = A_2 - A_3$

This gives

$A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)$

Expand

$A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2$

Evaluate the difference

$A = \frac 12r^2$

Recall that the area of the isosceles triangle is

$A_1 = \frac 12r^2$

By comparison, we have:

$A = A_1 = \frac 12r^2$

This means that the areas of the lune and the isosceles triangle are equal

Read more about areas at:

brainly.com/question/27683633

#SPJ1

5 0

1 year ago

A border collie is on sale at a 20% discount. If it normally sells for $475.00, what is the sale price?

tatyana61 [14]

What you have to do is multiply 475.00 by .20. Then from there yousubtract 475-(475*.20). From there you will get the answer.

8 0

3 years ago

Jonathan deposited $10,000 into a new savings account with a simple interest rate of 3.8%. If account has earned $2,470 in inter

vichka [17]

Answer:

6.5 years

Step-by-step explanation:

the amount depositited times percent diveded by the intrest is the years

5 0

3 years ago

Fiind the value of x between 0 and 360 <br>for question 5sin 2x=7cos2x

Degger [83]

Answer:

x=pi*n/2+1/2arctan(7/5)

Step-by-step explanation:

5sin(2x)=7cos(2x)

5tan(2x)=7/5

2x=pi*n+arctan(7/5)

x=pi*n/2+1/2arctan(7/5) for n e Z

6 0

3 years ago

0.5 ft<br> 0.4 ft<br> 0.8 ft<br> Area of base =

beks73 [17]

Answer:

it may can be 0.16 ft

Step-by-step explanation:

0.5 x 0.4 = 0.2

0.8 x 0.2 = 0.16

7 0

2 years ago

Read 2 more answers