Mathematics: Arectangle is bounded by the x-axis and the semicircle y=sqrt(36-x^2) write the area a of the rectangle as a function of x

Arectangle is bounded by the x-axis and the semicircle

reinasuarez964

12.03.2022

we are given

A rectangle is bounded by the x-axis and the semicircle y=sqrt(36-x^2)

we can see that

length=L=2x

width=W=y

we know that

area of rectangle is length*width

A=L*W

now, we can plug values

A=2x*y

$A=2x\sqrt{36-x^2}$ ..............Answer

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cjp271

30.05.2020

Option D.

Step-by-step explanation:

Given information: KLMN is parallelogram, K(7,7), L(5,3), M(1,1) and N(3,5).

Diagonals of a parallelogram bisect each other.

If diagonals of a parallelogram are perpendicular to each other then the parallelogram is a rhombus.

If a line passes through two points (x_1,y_1) and (x_2,y_2) , then the rate of change is

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of KM is

$m_1=\frac{1-7}{1-7}=1$

Slope of LN is

$m_2=\frac{5-3}{3-5}=-1$

The product of slopes of two perpendicular lines is -1.

Find the product of slopes.

$m_1\cdot m_2=1\cdot (-1)=-1$

The product of slopes of KM and NL is -1. It means diagonals are perpendicular and KLMN is a rhombus.

Therefore, the correct option is D.

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