All categories

3 years ago

Compare the two functions to see which has a greater rate of change. Function 1

Mathematics

1 answer:

AleksAgata [21]3 years ago

7 0

Function 2 has greater rate of change

Step-by-step explanation:

In order to find the rate of change we have to covert the given linear functions in slope-intercept form

Function 1:

$-2x+5y = 10$

Adding 2x on both sides

$-2x+5y+2x = 2x+10\\5y = 2x+10$

Dividing both sides by 5

$\frac{5y}{5} = \frac{2x+10}{5}\\y = \frac{2}{5}x +\frac{10}{5}\\y = \frac{2}{5}x+2$

Let m1 be rate of change of function 1:

$m_1 = \frac{2}{5}$

Function 2:

$-6x+3y = 18$

Adding 6x on both sides

$-6x+3y+6x = 6x+18\\3y = 6x+18$

Dividing both sides by 3

$\frac{3y}{3} = \frac{6x+18}{3}\\y = \frac{6x}{3} + \frac{18}{3}\\y= 2x+6$

Let m2 be the slope of function 2

$m_2 = 2$

As we can see that

$m_2>m_1$

Function 2 has greater rate of change

Keywords: Linear functions, slope

Learn more about functions at:

#LearnwithBrainly

You might be interested in

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a

Margaret [11]

Suppose x quarts of the 50% solution
0.5x+0.2*20=0.4(x+20)
0.5x+4=0.4x+8
0.1x=4
x=40

7 0

3 years ago

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the ye

Salsk061 [2.6K]

The average maximum would be C. 76.8 degrees

4 0

3 years ago

What's 22 + 4? ghdjdhsbsjs

Debora [2.8K]

Answer:LOL 26

Step-by-step explanation: 22=4 IS LIKE EASY BUT IF YOU FORGOT THEN THATS FINE

4 0

4 years ago

What is the slope of the line (-5,-7) and (4,-1)

forsale [732]

Answer:

2/3

Step-by-step explanation:

slope = change in y / change in x = (-7-(-1))/(-5-4) = (-6)/(-9) = 2/3

3 0

3 years ago

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 − x^2? show your

LUCKY_DIMON [66]

Answer:

Option B.

Step-by-step explanation:

The given curve is

$y=27-x^2$

We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve $y=27-x^2$ .

Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .

Length of the rectangle = 2x

Width of the rectangle = y

Area of a rectangle is

$Area=Length\times width$

$Area=2x\times y$

Substitute the value of y from the given equation.

$Area=2x(27-x^2)$

$A=54x-2x^3$ .... (1)

Differentiate with respect to x.

$\frac{dA}{dx}=54-6x^2$

Equate $\frac{dA}{dx}=0$ , to find the critical points.

$0=54-6x^2$

$6x^2=54$

Divide both sides by 6.

$x^2=9$

$x=\pm 3$

The value of x can not be negative because side length can not be negative.

Substitute x=3 in equation (1).

$A=54(3)-2(3)^3$

$A=162-54$

$A=108$

The area of the largest rectangle is 108 square units.

Therefore, the correct option is B.

7 0

3 years ago