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3 years ago

Which phrase describes a nonlinear function?

1 answer:

5 0

The only non-linear equation from your choices is the area of a circle as it is:

A=πr^2 and if you take the derivative of A you have:

dA/dr=2πr

So the rate of change changes as r changes, it is not constant thus the function has acceleration, so velocity changes.

This is in contrast to any linear equation which is of the form:

y=mx+b now taking the derivative you see that:

dy/dx=m, now m is a constant value, which means that there is no acceleration and the velocity remains constant.

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Graph the direct variation equation. y=9x

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Use the slope 9 and then go through (0,0)

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3 years ago

Mar 10, 11:28:13 PM

Virty [35]

Answer:

s249

Step-by-step explanation:

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3 years ago

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kondor19780726 [428]

Answer:

13. 12000

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3 years ago

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A culture started with 3,000 bacteria. After 8 hours, it grew to 3,300 bacteria. Predict how many bacteria will be present after

Sav [38]

Answer:

$3,462\ bacteria$

Step-by-step explanation:

In this problem we have a exponential function of the form

$y=a(b^x)$

where

x is the time in hours

y is the numbers of bacteria

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

we have that

$a=3,000\ bacteria$

For x=8, y=3,300

substitute in the exponential function

$3,300=3,000(b^8)$

solve for b

$1.1=(b^8)$

$b=\sqrt[8]{1.1}$

$b=1.0120$

Find the value of r

$r=b-1=1.0120-1=0.0120=1.20\%$

The equation is equal to

$y=3,000(1.012^x)$

For x=12 hours

substitute the value of x in the equation

$y=3,000(1.012^{12})$

$y=3,462\ bacteria$

8 0

4 years ago

Indicate the equation of the given line in standard form. Show all your work for full credit. the line containing the median of

alukav5142 [94]

Answer:

* The equation of the median of the trapezoid is 10x + 6y = 39

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

- The standard form of the linear equation is Ax + BC = C, where

A , B , C are integers and A , B ≠ 0

- The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

- It has two properties:

# It is parallel to both bases

# Its length equals half the sum of the base lengths

* Lets solve the problem

- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)

- Lets find the slope of the 4 sides two find which of them are the

parallel bases and which of them are the non-parallel bases

# The side RS

∵ $m_{RS}=\frac{8-5}{1 - (-1)}=\frac{3}{2}$

# The side ST

∵ $m_{ST}=\frac{-2-8}{7-1}=\frac{-10}{6}=\frac{-5}{3}$

# The side TU

∵ $m_{TU}=\frac{0-(-2)}{2-7}=\frac{2}{-5}=\frac{-2}{5}$

# The side UR

∵ $m_{UR}=\frac{5-0}{-1-2}=\frac{5}{-3}=\frac{-5}{3}$

∵ The slope of ST = the slop UR

∴ ST// UR

∴ The parallel bases are ST and UR

∴ The nonparallel sides are RS and TU

- Lets find the midpoint of RS and TU to find the equation of the

median of the trapezoid

∵ The median of a trapezoid is a segment that joins the midpoints of

the nonparallel sides

∵ The midpoint of RS = $(\frac{-1+1}{2},\frac{5+8}{2})=(0,\frac{13}{2})$

∵ The median is parallel to both bases

∴ The slope of the median equal the slopes of the parallel bases = -5/3

∵ The form of the equation of a line is y = mx + c

∴ The equation of the median is y = -5/3 x + c

- To find c substitute x , y in the equation by the coordinates of the

midpoint of RS

∵ The mid point of Rs is (0 , 13/2)

∴ 13/2 = -5/3 (0) + c

∴ 13/2 = c

∴ The equation of the median is y = -5/3 x + 13/2

- Multiply the two sides by 6 to cancel the denominator

∴ The equation of the median is 6y = -10x + 39

- Add 10x to both sides

∴ The equation of the median is 10x + 6y = 39

* The equation of the median of the trapezoid is 10x + 6y = 39

7 0

4 years ago