Which ratio is equal to 27 : 81?

Simplify the difference quotient f ( x + h ) â f ( x ) h for the function f ( x ) = 6 x â x 2

ladessa [460]

Answer:

final answer is 6

Step-by-step explanation:

Given $f(x)=6x-2$

To find the difference quotient use formula

$\frac{f(x+h)-f(x)}{h}$

$f(x)=6x-2$

$f(x+h)=6(x+h)-2=6x+6h-2$

Now plug it in the formula

$\frac{f(x+h)-f(x)}{h}$

$\frac{6x+6h-2-(6x-2)}{h}$

$\frac{6x+6h-2-6x+2)}{h}$

$\frac{6h}{h}$

6

5 0

3 years ago

In the xy-plane, a line crosses the y-axis at the point (0, 3) and passes through the point (4, 5). Which is the equation of the

Gelneren [198K]

Answer:D

Step-by-step explanation:

4 0

2 years ago

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboa

Aliun [14]

Given the dartboard of diameter $20in$ , divided into 20 congruent sectors,

The central angle is $18^\circ$

The fraction of a circle taken up by one sector is $\frac{1}{20}$

The area of one sector is $15.7in^2$ to the nearest tenth

The area of a circle is given by the formula

$A=\pi r^2$

A sector of a circle is a fraction of a circle. The fraction is given by $\frac{\theta}{360^\circ}$ . Where $\theta$ is the angle subtended by the sector at the center of the circle.

The formula for computing the area of a sector, given the angle at the center is

$A_s=\dfrac{\theta}{360^\circ}\times \pi r^2$

<h3>Given information</h3>

We given a circle (the dartboard) with diameter of $20in$ , divided into 20 equal(or, congruent) sectors

<h3>Part I: Finding the central angle</h3>

To find the central angle, divide $360^\circ$ by the number of sectors. Let $\alpha$ denote the central angle, then

$\alpha=\dfrac{360^\circ}{20}\\\\\alpha=18^\circ$

<h3>Part II: Find the fraction of the circle that one sector takes</h3>

The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by $360^\circ$ . The angle has already been computed in Part I (the central angle, $\alpha$ ). The fraction is

$f=\dfrac{\alpha}{360^\circ}\\\\f=\dfrac{18^\circ}{360^\circ}=\dfrac{1}{20}$